Optimization of Origami Inspired Static and Active ...

Optimization of Origami Inspired Static and Active Mechanical Metamaterial

by

Mohamed Ali Emhmed Kshad

A thesis submitted in conformity with the requirements for the degree of Doctoral of Philosophy

Department of Mechanical and industrial Engineering University of Toronto

© Copyright by Mohamed Ali Emhmed Kshad 2019

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Optimization of Origami Inspired Static and Active Mechanical

Metamaterial


Doctor of Philosophy

Department of Mechanical and Industrial Engineering

University of Toronto

2019

Abstract

Origami-inspired materials provide effective solutions to control the mechanical properties of

sandwich core structures, due to their outstanding structural features and due to the unique

capacity of elastic deformation of its elements that are able to fold and unfold at different scales

during the loading process. Both the geometrical features and the properties of the parent

material that used to produce the origami structures are the most important factors required for

tailoring the designed origami core with the target application. To eliminate the fracture and the

abrupt stress change in the designed origami core elements, it is important to consider the parent

material properties and behavior. There are two important challenges that should be considered

in designing origami cores, the geometrical features of the origami tessellation and the material

used to produce the origami unit cells and cores. Three dimensional origami cores can be

fabricated by folding two dimensional flat sheets into three dimensional cores, or by pre-folding

the origami features using a molding process. This research is devoted to investigate pre-folded

origami cores made of polymeric materials for damping applications. Both passive and active

properties of the designed unit cells were investigated in this research. Two different origami

patterns were considered in the research, Miura and Ron-Resch-like origami structures. Different

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material blends were used to fabricate pre-folded origami features and correlate with the

mechanical properties of the fabricated cores. Another way of preparing pre-folded origami cores

is by using fused deposition modeling, in which different Ron-Resch-like cores with different

geometrical parameters were designed and characterized for compression and impact load

absorption. The designed origami cores were numerically simulated and compared with the

experimental results. This motivated to include the viscoelastic behavior of the polymeric parent

material at elevated temperature and simulate the cores’ unit cell using periodic boundary

condition; the actual skeleton of the origami unit cell structure was represented in order to

capture the mechanical behavior.

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Acknowledgments

I owe my deepest appreciation to my late father and mother, who instilled in me the love

of science and perseverance. I owe them whatever I have achieved whatever I will achieve. To

them, I dedicate this work.

“And lower unto them the wing of submission through mercy, and say: My Lord! Have mercy on

them both as they did care for me when I was little”.

( Al-Isra24)

I would like to express my sincere grateful and thanks to my wife Rabyaa for her

unconditional support. Her endless love and patience made the hard times easier and the good

times adorable. Furthermore, I would expand my thanks to my kids, Owais, Omama, and

Almuthanna, who bring the brightness, love, and make us happiness. Moreover, I would like to

extend my thanks and appreciation to my siblings for their support and encouragement.

I would like to express my sincere gratitude and appreciation to my supervisor, Professor

Hani E. Naguib for his excellent supervision and continuous guidance during my research years.

Through his vision, his insights, and his cheerful personality I learned a lot and I enriched my

knowledge, not just in my Ph.D. research but in my entire life. I can proudly say I was so lucky

meeting with a great person like him. I greatly indebted all what I achieved in my Ph.D. journey.

I would like to thank my Ph.D. committee members, Professor Chul B. Park, and

Professor Lidan You, who have given me valuable feedbacks and suggestions during my Ph.D.

research.

I am also grateful to my previous and current friends in SAPL group, especially, Farooq,

Anwer, Harvey, Arturo, Gary, Nazanin, Ahmed, Harison, and all other members of SAPL with

whom I worked in very friendly atmosphere. They all were helpful and ready to give a valuable

feedback whenever needed.

I acknowledge with gratitude to the following agencies for their financial support: the

Libyan Ministry of Higher Education and scientific research, Tripoli, Canadian Bureau for

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International Education (CBIE), And the Natural Science and Engineering Research Council

(NSERC) of Canada, the Canada Research Chair Program.

Lastly and above all, I would always grateful to Allah, the Almighty, the Creator, and the

Unlimited Source of gifts, for His infinite gifts in life, His mercy, His guidance, and His constant

help.


Toronto, Canada

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Table of Contents

Acknowledgments ..................................................................................................................... iv

Table of Contents ...................................................................................................................... vi

List of Tables ............................................................................................................................ xi

List of Figures .......................................................................................................................... xii

Chapter 1. ................................................................................................................................... 1

Introduction ................................................................................................................................ 1

1.1 Preamble ......................................................................................................................... 1

1.2 Definition ....................................................................................................................... 2

1.3 Fabrication of Origami Panels ......................................................................................... 3

1.4 Problem Statement and Motivation ................................................................................. 4

1.5 Objectives and Scope of Work ........................................................................................ 5

1.6 Thesis Organization ........................................................................................................ 5

1.7 References ...................................................................................................................... 9

Chapter 2. ................................................................................................................................. 13

Material Selection and Characterization .................................................................................... 13

2.1 Introduction .................................................................................................................. 13

2.2 Material Processing and Characterization ...................................................................... 14

2.3 Experimental Work ....................................................................................................... 16

2.3.1 Material Blending Morphology ......................................................................... 16

2.3.2 Differential Scanning Calorimetry (DSC) Test .................................................. 16

2.3.3 Dynamical Mechanical Analysis (DMA) Test ................................................... 16

2.3.4 Rheological Test................................................................................................ 16

2.4 Results and Discussion.................................................................................................. 17

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2.4.1 SEM Morphology of Blended Polymers ............................................................ 17

2.4.2 DSC Test Results .............................................................................................. 17

2.4.3 DMA Test Results ............................................................................................. 18

2.4.4 Rheological Properties....................................................................................... 19

2.5 Conclusion .................................................................................................................... 21

2.6 References .................................................................................................................... 22

Chapter 3. ................................................................................................................................. 25

Development and Modeling of Multi-phase Polymeric Origami Inspired Architecture by

Using Pre-molded Geometrical Features .............................................................................. 25

3.1 Introduction .................................................................................................................. 26


3.2.1 Materials Processing.......................................................................................... 28

3.2.2 Fabrication of Origami Structures ...................................................................... 28

3.2.3 Miura Origami Unit Cell and Core Configuration .............................................. 29

3.2.4 Compression Test .............................................................................................. 30

3.2.5 Impact Test ....................................................................................................... 31

3.3 Simulation and Analysis ............................................................................................... 32

3.3.1 Compression Simulation.................................................................................... 32

3.3.2 Impact Event Simulation ................................................................................... 32


3.4.1 Compression Test Results.................................................................................. 33

3.4.2 Impact Test Results ........................................................................................... 37

3.4.3 Finite Element Results ....................................................................................... 40

3.5 Conclusion .................................................................................................................... 43

3.6 References .................................................................................................................... 45

Chapter 4. ................................................................................................................................. 47

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Carbon Nano Fibers Reinforced Composites Origami Inspired Mechanical Metamaterials

with Passive and Active Properties....................................................................................... 47

4.1 Introduction .................................................................................................................. 48


4.2.1 Materials ........................................................................................................... 50

4.2.2 Material Blends Microstructure ......................................................................... 52

4.2.3 Fabrication process ............................................................................................ 53

4.2.4 Differential Scanning Calorimetry (DSC) Test .................................................. 54

4.2.5 Dynamic Mechanical Analysis (DMA) Test ...................................................... 54

4.2.6 Passive Properties of Composite Origami Cores ................................................ 55

4.2.7 Active Properties ............................................................................................... 56


4.3.1 Thermal Properties of Composite Material Blends ............................................. 56

4.3.2 Passive Properties .............................................................................................. 60

4.3.3 Active Properties ............................................................................................... 65

4.4 Conclusion .................................................................................................................... 67

4.5 References .................................................................................................................... 68

Chapter 5. ................................................................................................................................. 72

3D Printing of Ron-Resch-Like Origami Cores for Compression and Impact Load Damping ... 72

5.1 Introduction .................................................................................................................. 73

5.2 Experimental work ........................................................................................................ 74

5.3 Fused Deposition Modeling (FDM) for Fabricating Origami Structures ........................ 76

5.4 Mechanical Testing Procedure ...................................................................................... 79

5.4.1 Compression Test .............................................................................................. 79

5.4.2 Impact Test ....................................................................................................... 80

5.5 Modeling of Ron-Resch-Like Origami Panels ............................................................... 80

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5.5.1 Compression Test Simulation ............................................................................ 80

5.5.2 Impact Test Simulation ...................................................................................... 80

5.6 Shape Recovery of Ron-Resch-Like Origami Unit Element .......................................... 81


5.7.1 Compression test results .................................................................................... 81

5.7.2 Impact Test Results ........................................................................................... 86

5.7.3 FEM Simulation Results .................................................................................... 87

5.7.4 Shape Recovery Results .................................................................................... 92

5.8 Conclusion and Future Directions ................................................................................. 94

5.9 References .................................................................................................................... 96

Chapter 6. ................................................................................................................................. 99

Modeling and Characterization of Viscoelastic Origami Structures Using Temperature

Variation-based Model ......................................................................................................... 99

6.1 Introduction .................................................................................................................100

6.2 Experimental Procedure ...............................................................................................101

6.3 Finite Element Modeling..............................................................................................102

6.3.1 Finite Element Geometry and Boundary Conditions .........................................102

6.3.2 Viscoelastic Materials in ABAQUS ..................................................................104

6.4 Results and Discussion.................................................................................................106

6.4.1 Compression Test Results of Origami Unit Cell ...............................................107

6.4.2 Correlation Analysis and Regression ................................................................108

6.4.3 Unit Cell Deformation and Stress .....................................................................110

6.4.4 Origami Panel Finite Element Results ..............................................................114

6.5 Conclusion ...................................................................................................................120

6.6 References ...................................................................................................................121

Chapter 7. ................................................................................................................................123

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Conclusion and Recommendations ..........................................................................................123

7.1 Concluding Remarks ....................................................................................................123

7.2 Major Contributions .....................................................................................................125

7.3 Recommendations ........................................................................................................126

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List of Tables

Table ‎3.1 Material blends density and origami volumetric density. ........................................... 30

Table ‎3.2 Comparison of specific modulus of elasticity of solid blended material and origami

cores. ........................................................................................................................................ 35

Table ‎3.3 Comparison of maximum impact force transferred. ................................................... 39

Table ‎4.1 The physical, mechanical and the thermal properties used to fabricate origami cores. 51

Table ‎4.2 The DSC Results of the Material blends. ................................................................... 57

Table ‎4.3 Comparison between the maximum force transferred by composite origami cores and

other plane materials................................................................................................................. 64

Table ‎5.1 The dimensions of the designed Ron-Resch-like origami unit cells. .......................... 76

Table ‎5.2 Comparison of maximum impact force transferred. ................................................... 87

Table ‎6.1 Fitting parameters of one-term Prony series according to equation (8). .................... 107

Table ‎6.2 Summary of experimental/fitting results. ................................................................. 109

Table ‎6.3 Correlation coefficients between selected parameters. ............................................. 109

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List of Figures

Figure ‎1.1 Miura origami unit cell dimensions and the three folding states of the Miura panel

[15]. ........................................................................................................................................... 4

Figure ‎2.1 Schematic of compounding process used to produce material blends ....................... 15

Figure ‎2.2 Comparison of the density of the material blends ..................................................... 15

Figure ‎2.3 SEM morphology of blended polymers, PLA/TPU wt %. a) 100/0, b) 80/20, c) 65/35,

d) 50/50, e) 20/80, and f) 0/100................................................................................................. 17

Figure ‎2.4 DSC thermosgrams for PLA/TPU wt % blends. ....................................................... 18

Figure ‎2.5 Comparison of the storage modules of the polymers blends. .................................... 19

Figure ‎2.6 Comparison of the loss modules of the polymers blends. ......................................... 19

Figure ‎2.7 Rheological properties of PLA/TPU wt % blends (storage modulus). ....................... 20

Figure ‎2.8 Rheological properties of PLA/TPU wt % blends (loss modulus). ............................ 20

Figure ‎2.9 Rheological properties of PLA/TPU wt % blends (complex viscosity). .................... 21

Figure ‎3.1 a) Multi-stage compression mold used to fabricate origami cores b) The geometrical

parameters of fabricated origami cores. .................................................................................... 29

Figure ‎3.3 The meshed geometry of the origami a) compression simulation, b) impact simulation.

................................................................................................................................................. 33

Figure ‎3.4 Compression stress-strain relation of origami core structure. .................................... 34

Figure ‎3.5 . Modulus of elasticity and strength of origami cores. .............................................. 34

Figure ‎3.6 Comparison of maximum stress of origami cores and the deflection at maximum

stress. ....................................................................................................................................... 34

Figure ‎3.7‎Comparison‎of‎origami‎cores’‎toughness. ................................................................ 35

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Figure ‎3.8 SEM images of fracture surface of Neat PLA origami core with magnification a) 40X,

b) 130X, c) 750X. ..................................................................................................................... 36

Figure ‎3.9 SEM images of fracture surface of 80/20 PLA/TPU origami core with magnification

a) 40X, b) 130X, c) 750X. ........................................................................................................ 36

Figure ‎3.10 Sample of impact force for neat PLA. .................................................................... 38

Figure ‎3.11 Maximum transferred impact force. ....................................................................... 38

Figure ‎3.12 Maximum impact energy transferred. ..................................................................... 39

Figure ‎3.13 The change of the results error (%) by changing the mesh size. .............................. 40

Figure ‎3.14 Comparison of Von-Misses stress values for origami cores of different material

blends. ...................................................................................................................................... 41

Figure ‎3.15 Von-Misses stress distribution on origami cores a) Neat PLA, b) 80/20 PLA/TPU, c)

50/50 PLA/TPU, and d) neat TPU. ........................................................................................... 41

Figure ‎3.16 The total energy, internal core energy, and the energy dissipated by origami cores. 42

Figure ‎3.17 Reaction force, and the directional deformation. .................................................... 42

Figure ‎3.18 Directional displacement of origami core a) PLA b) TPU. ..................................... 43

Figure ‎4.1 SEM micrographs of composite blends, magnification factor 20000X, a) PLA with 1

wt% CNF, b) PLA with 3wt% CNF, c) PLA with 5 wt% CNF, d) 80/20 PLA/PTU with 5 wt%

CNF, e) 50/50 PLA/PTU with 5 wt% CNF, f) TPU with 5 wt% CNF. ...................................... 52

Figure ‎4.2 a) Multi-stage compression mold used to fabricate origami cores, b) Composite

origami structures made by molding process............................................................................. 54

Figure ‎4.3 Composite origami cores placed between thick-rigid plates in the compression test. 55

Figure ‎4.4 Composite origami core sandwiched between two plates, b) Impact test setup. ........ 56

Figure ‎4.5 Thermal behavior of composite blends with CNF. ................................................... 58

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Figure ‎4.6 Storage and loss moduli of PLA/TPU blends with CNF. .......................................... 59

Figure ‎4.7 Modulus of elasticity of the CNF reinforced blended composite parent materials. .... 61

Figure ‎4.8 Comparison the modulus of elasticity of the pure blended origami [35] with composite

origami cores. ........................................................................................................................... 61

Figure ‎4.9 Comparison the strength of pure blended origami [35] with composite origami cores.

................................................................................................................................................. 61

Figure ‎4.10 Toughness of composite origami cores................................................................... 61

Figure ‎4.11 (a) Fractured PLA+1%CNF sample under the point of impact, (b) Propagation of the

fracture through crease line on a PLA+1%CNF sample, (c) fractured PLA+3%CNF sample. ... 62

Figure ‎4.12 Sample of impact force-time response. ................................................................... 64

Figure ‎4.13 Comparison of the max. force transferred by pure blended origami cores [35] with

composite origami cores ........................................................................................................... 64

Figure ‎4.14 Comparison of maximum impact energy transferred by pure blended origami cores

[35] with composite origami cores. ........................................................................................... 64

Figure ‎4.15 Cracked composite Origami unit cell made of (PLA + 3wt % CNF) ...................... 66

Figure ‎4.16 Deformed composite origami unit cell made of low percentage of CNF (PLA +

0.1wt % CNF) ......................................................................................................................... 66

Figure ‎4.17 Stress relaxation test of composite origami sample made of PLA + 0.1wt% CNF .. 66

Figure ‎4.18 Recovery shape of composite origami sample made of PLA + 0.1wt % CNF ......... 66

Figure ‎4.19 The origami unit cell recovery (height) .................................................................. 67

Figure ‎5.1 The designed Ron-Resch-like origami unit elements, a) RR – 3, b) RR – 4, and c)

RR – 6. .................................................................................................................................... 74

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Figure ‎5.2 The designed tessellations of Ron-Resch-like origami panels, a) RR – 3 – 15, b)

RR – 3 – 30, c) RR – 3 – 60, d) RR – 6 – 15, e) RR – 6 – 30, f) RR – 6 – 60, g) RR – 4 – 15, h)

RR – 4 – 30, i) RR – 4 – 60. ..................................................................................................... 75

Figure ‎5.3 RR-3-30 model, (a) a 3D view of Ron-Resch-like origami panel (b) the in-plane

dimensions in mm of origami panel, and (c) the basic element configuration of the origami. .... 76

Figure ‎5.4 (a) Fabricated Ron-Resch-like origami panel (b) Ron-Resch-like element................ 77

Figure ‎5.5 3D-printed Ron-Resch-like origami panel, a) RR – 3 – 15, b) RR – 3 – 30, c)

RR – 3 – 60, d) RR – 6 – 15, e) RR – 6 – 30, f) RR – 6 – 60, g) RR – 4 – 15, h) RR – 4 – 30, i)

RR – 4 – 60. ............................................................................................................................. 78

Figure ‎5.6 3D-printed Ron-Resch-Like origami unit cell, a) RR – 3 – 15, b) RR – 3 – 30, c)

RR – 3 – 60, d) RR – 6 – 15, e) RR – 6 – 30, f) RR – 6 – 60, g) RR – 4 – 15, h) RR – 4 – 30, i)

RR – 4 – 60. ............................................................................................................................. 79

Figure ‎5.7 Compression model of the Ron-Resch-like core panel (RR – 3 – 15). ...................... 81

Figure ‎5.8 Impact model of the Ron-Resch-Like core panel (RR – 3 – 15)................................ 81

Figure ‎5.9 Compressive stress-strain relations of a) RR – 3, b) RR – 4, c) RR – 6, d) Comparison

of the compressive modulus...................................................................................................... 82

Figure ‎5.11 Plastic deformation on the tip of the star tuck of the Ron-Resch-like origami element.

................................................................................................................................................. 83

Figure ‎5.12 Transferred impact force. ....................................................................................... 87

Figure ‎5.13 The maximum impact forces transferred by the Ron-Resch-like panels. ................. 87

Figure ‎5.14 The compressive deformation of the RR – 3 – 15 model compared with the tested

sample. ..................................................................................................................................... 88

Figure ‎5.15 a) The total compressive deformation of the RR – 3 – 15 model, b) the directional

compressive deformation (y-direction) of the RR-3-30 model. .................................................. 89

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Figure ‎5.16 Comparison of a) maximum total deformation, b) maximum equivalent stress. ...... 89

Figure ‎5.17 . a) The total deformation due to impact event (RR – 3 – 15), b) the equivalent von-

Mises Stress distribution on the model (RR – 6 – 15). ............................................................... 89

Figure ‎5.18 Comparison of the maximum transferred force by impact. ..................................... 90

Figure ‎5.19 The deformation of the star-tuck-edges. ................................................................. 91

Figure ‎5.20 The deformation of the star – tuck branches of Ron-Resch-like origami panels. ..... 91

Figure ‎5.21 The FEM results of the maximum deformation of the Ron-Resch tested models .... 92

Figure ‎5.22 The three phases of the geometry changes during the shape memory effect test. .... 92

Figure ‎5.23 Compression and stress relaxation results of the Ron-Resch-like origami unit

element, a) compression of RR – 3, b) stress relaxation of RR-3, c) compression of RR – 4,

d) stress relaxation of RR – 4, e) compression of RR – 6, and f) stress relaxation of RR - 6 ...... 93

Figure ‎5.24 Shape recovery of the Ron-Resch-like origami unit element, a) RR-3, b) RR-4, c)

RR-6, d) comparison of the height recovery ratio. ..................................................................... 94

Figure ‎6.1 The representative unit cell (RUC) of the origami structure. .................................. 103

Figure ‎6.2 Application of periodic boundary conditions in ABAQUS. .................................... 104

Figure ‎6.3 . Experimental results of the relaxation modulus to one-term Prony series, a) T=25 C,

b) T=35 C, c) T=45 C, d) T=55 C. ..................................................................................... 107

Figure ‎6.4 Compression behavior of the origami unit cell at different temperatures ................ 108

Figure ‎6.5 Stress-strain relation of the simulated origami unit cell .......................................... 111

Figure ‎6.6 Comparison of experimental and FEM model of the modulus of elasticity of origami

model. .................................................................................................................................... 112

Figure ‎6.7 Total deformation of the origami unit cell a) T=25 C, b) T=35 C, c) T=45 C, d)

T=55 C. 112

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Figure ‎6.8 Deformation at y direction U2 of the origami unit cell a) T=25 C, b) T=35 C, c)

T=45 C, d) T=55 C. ............................................................................................................. 113

Figure ‎6.9 Von-Mises- stress on origami unit cell a) T=25 C, b) T=35 C, c) T=45 C, d)

T=55 C. ................................................................................................................................ 114

Figure ‎6.10 Origami panel, a) geometrical features, b) meshed model .................................... 115

Figure ‎6.11 The auxetic behavior of the origami panel, a) along the X-axis, b) along the Z-axis

............................................................................................................................................... 115

Figure 6.12 Stress - Strain of origami panel at different temperatures ..................................... 116

Figure ‎6.13 Modulus of elasticity of origami panel at different temperatures .......................... 116

Figure ‎6.14 The total deformation of the origami panel........................................................... 117

Figure ‎6.15 The directional deformation of the origami panel along the X-axis ...................... 118

Figure ‎6.16 The directional deformation of the origami panel along the Y-axis ...................... 119

Figure ‎6.17 Von-Mises stress generated in the simulated origami panel .................................. 119

1

Chapter 1.

Introduction

1.1 Preamble

Metamaterials are artificial materials engineered to have superiority over the conventional

materials; they gain their properties form the shape and the geometry of how the material is

arranged rather than from the constituting material itself [1–3]. However, metamaterials refer to

the materials that behave differently from the materials in nature; their use in engineering

applications is still limited. The rapid development in this area has shown that the way materials

are arranged and fabricated can yield different properties than the properties of their

composition. Adding local texture (such as corrugation, folds, dimples, etc.) to a thin-walled

sheet can extend and favorably modify the mechanical properties to suit specific applications [4].

The idea of folding papers to create three dimensional structures came early from Japanese

origami art, in which two-dimensional flat sheet folded through different patterns to produce 3D

structures. The main challenges in designing origami metamaterials are selecting the proper

origami patterns, and the folding process to create non-overlapping structural units, as well as

tailoring of the material properties that can be used to produce origami elements and the

connectivity between these elements. The recent research in the development of mechanical

metamaterials showed that there is a vast increase in the development of mechanical

metamaterials. The ability of origami structures in force damping due to the high elastic

deformation of its parts in the folding-unfolding process. Theoretical, mathematical, and

numerical studies have been extensively done in previous research [5-13], Origami pattern based

on Miura origami design has gained the most intention due to its simplicity [2,3,14-20].

Moreover, periodic origami structures have shown high performance in l lightweight structures

[14,21,22]. Most of the previous research focused mainly on the origami made from paper sheets

or thin metallic sheets while the polymeric origami has gained less attention. In this research, the

main objective is to develop polymeric origami structures that still have the least amount of

interest in literature, by using pre-folded process, because it is easier in manufacturing compared

2

to paper folding process, and then to investigate the mechanical passive and active behavior of

different origami configurations.

1.2 Definition

The property that characterizes the unconventional behavior of mechanical metamaterials is

Poisson's ratio. While the majority of conventional materials have positive Poisson's ratio,

conventional materials (metamaterials) have negative Poisson's ratio (NPR) [23-24].

Metamaterial is composed of assemblies of individual elements made from classical materials

such as metals or plastics, but they are arranged in certain patterns. The properties of mechanical

metamaterials arise almost exclusively from the geometry of the constituent folds, tessellation

patterns, folding angles, and the constraint of the isometric deformations [25]. Their geometry,

size, orientation, and arrangement affect the mechanical behavior in an unconventional manner,

creating material properties which are not achieved with conventional materials [25]. NPR

materials become stiffer and stronger when the amplitude of the load increases. The

mathematical and theoretical research progress in foldable structures paves new ways of

fabricating and modeling geometrically complex origami inspired metamaterials. The idea of

folding papers came early from Japanese origami art, in which two-dimensional flat sheet folded

through different patterns to produce 3D structures, and it was a natural inspiration in which

many natural threes leaves has the folding-unfolding through crease lines [26]. The produced 3D

origami structures are identified by the crease patterns and the folding angles [2]; there are

limitless ways to design crease patterns, and therefore to produce different 3D origami forms.

Depending on the design of the crease patterns and the folding angles, the 3D origami structures

will have different mechanical properties [2]. Many origami patterns were proposed to create 3D

structures, such as Miura origami pattern and Ron-Resch pattern. Miura origami was proposed

by Miura in the 1970s for core structure applications and for solar panels [2,3,15–17], figure 1.1

shows the details of Miura origami unite cell and the Miura origami sheet structure folding

states. The Ron-Resch origami pattern proposed by Resch is also one of the most interesting

origami patterns that have attracted attention due to its way of forming curved panels during the

folding process [2,27,28]. Origami structures are known to afford large macroscopic

deformation, force redistribution, and energy damping.

3

1.3 Fabrication of Origami Panels

The most common origami structures prepared from flat 2D sheet turned to a 3D structure by

complex folding process. The process of creating three-dimensional origami structures starts by

designing the folding patterns, then folding the small pattern elements through the crease lines.

Many research has been conducted previously to develop the fabrication process of origami

structure through the folding process, in which the 3D panels can be created from 2D sheets,

without overlapping of the facets of the unit cell structure [29,30]. Elsayed et. al, proposed a

fabrication method for sheet materials folding, which allowed to fold in different patterns using

continuous manufacturing techniques [31]. Recently, the use of active structures has attracted

designers and engineers to utilize active materials for designing foldable origami structures.

Active materials are materials that have the ability to convert different forms of energy into

mechanical work [32]. Shape memory polymer, is a sort of active materials that has the

capability to recover the initial shape under external stimuli such as thermal energy [33]. They

are able to change form and can be programmed for different types of stimuli and also able to

present the shape changes [33,34]. The elastic behavior of SMPs allows the retention of a

temporary shape and recovers the original form. This is due to the existence of two different

segments in the structure of the polymer: the hard and the soft segments [33–36]. The hard

segment is responsible for the stabilization of the permanent shape while the soft segment allows

the structure to pass from permanent to temporary and from temporary to permanent states [33,

34]. Origami structures have promising spectrum of applications [21] such as sandwich cores,

aerospace structures, deployable structures, under trauma bulletproof, and other applications.

4

Figure ‎0.1 Miura origami unit cell dimensions and the three folding states of the Miura panel.

1.4 Problem Statement and Motivation

The main goal of the thesis is to develop pre-folded polymeric origami metamaterial cores that

can be qualified for a wide range of sectors that require lightweight structures, energy absorption,

self-activated structures and more. The fabrication and characterization of pre-folded origami

structure can avoid the need of folding process of a flat sheet to create the 3D origami structures,

the effect of the material used and the origami parameters are the most important factors that

should be addressed to design effective origami cores for energy dissipation and load damping.

The motivation of this work is:

Origami structures are known to afford large macroscopic deformation, force

redistribution, and energy damping.

Sandwiched cores as light-weight material can be combined with the origami properties

for compression and impact applications.

Shape memory polymers can be employed to produce active origami structure.

The accurate modeling helps to predict the behavior of origami unit cell based on the

properties of the parent material and the geometrical features of the origami tessellations.

5

1.5 Objectives and Scope of Work

The fabrication of origami structure cores is challenging, due to the complicity of the origami

patterns that make the folding process without overlapping of the unit cell faces difficult, also the

other‎reason‎is‎when‎the‎crease‎lines‎created‎they‎make‎weak‎connections‎between‎the‎elements’‎

faces in which the resultant 3D core cannot withstand the incoming loads. The main objective of

the thesis is developing metamaterial cores based on origami foldable structures using pre-folded

fabrication process, those cores can be used for applications that require lightweight materials,

energy absorption and self-activated structures.

The long term objective of this work is to optimize and develop a programmable design method

to manufacture origami structure metamaterial that can be utilized in high-end applications. This

objective can be reached by the following short terms objectives:

Fabricating and characterization different models of rigid origami structure using

polymer blends and reinforced composites for compression and impact properties.

Developing self-activated origami unit cell for folding/unfolding process by employing

shape memory polymers and correlate it with the thermomechanical properties of the

material blends.

Utilizing finite element modeling by using periodic boundary conditions and including

the viscoelastic properties to predict the mechanical properties and response of the

origami metamaterial cores.

1.6 Thesis Organization

The main body of the thesis was divided into three main parts; the first part (chapter 2, 3, and 4)

includes the fabrication of solid Miura origami structure. This part started with the material

selection and characterization of blended multiphase polymeric material, these materials selected

to fabricate the origami cores. The third chapter introduced the fabrication and modeling of

multi-phase pre-folded Miura origami cores by for compression and impact applications. The

fourth chapter included investigation of composite origami structure that made of carbon-

nanofibers reinforced multiphase polymers for passive and active properties. Both studies

included the experimental and finite element modeling of the origami cores for passive

6

mechanical properties. The second part of the thesis (chapter 5) introduced an investigation of

Ron-Resch-like pattern origami tessellation. The study provided a comparison of three origami

patterns with 3 different geometrical parameters. The origami unit cells and panels were

fabricated using fused deposition modeling. The third part of the thesis includes the modeling of

viscoelastic origami structure in elevated temperature, using prosodic boundary conditions.

Chapter 2 is devoted to studying the material selection and characterization of the blended

polymers. Two polymers, namely Poly-Lactic Acid (PLA) and thermoplastic polyurethane

(TPU),‎were‎selected‎to‎produce‎polymers’‎blends‎with‎different‎weight‎percentages. The weight

percentages of the PLA/TPU were 100/0, 80/20, 65/36, 50/50, 20/80, and 0/100. The study

provided the details of the blending process conditions, thermal and viscoelastic properties,

morphology, and the mechanical properties of the blended compositions.

In Chapter 3, the effect of the base material properties was investigated both experimentally and

numerically on the mechanical behavior of Miura-origami panels. The materials used in the

study for the origami cores were polymer blends composed of polylactic acid (PLA) and

thermoplastic polyurethane (TPU). PLA/TPU blend compositions are (100/0, 80/20, 65/35,

50/50, 20/80, and 0/100) as a weight percentage. The study shows the behavior of origami cores

under compression and impact tests and showed the energy absorbed by folded origami cores.

The highest specific energy absorption was demonstrated by 20/80 PLA/TPU blend in

compression and impact tests. The fractures in failed origami panels were observed in the crease

lines, (the folding edges), while the facets of the exhibit rigid body rotations.

Chapter 4: In order to enhance the mechanical properties of the blended material used to

fabricate origami structures, carbon nanofibers were used as a filler to overcome the drawback of

low modulus and strength of the origami cores. The weight percentages of CNF used are 1%,

3%, and 5%, and the material blends composition used were (100/0, 80/20, 65/35, 50/50, 20/80,

0/100) PLA/TPU as weight percentage. Direct compression molding process of origami features

was used to fabricate the tested samples. DSC test was conducted for the composite material

blends in order to predict the optimum fabrication process conditions. Also, DMA test for the

composite material blends was conducted to determine the viscoelastic properties. The fabricated

origami samples were then tested for compression and impact resistance; the results showed that

7

there is an improvement in the elastic modulus and the strength of composite origami cores

compared with pure blends origami cores.

Chapter 5 is devoted to studying the mechanical behavior of Ron-Resch-Like origami

tessellation made by 3D printing. The tested geometries are designed to create flat panels, three

different models were investigated, they are: three star tuck branches (RR-3), four star tuck

branches (RR-4), and six star tuck branches (RR-6), and three different folding angles were

considered for each model (15, 30, and 60), to investigate the effect of the folding angle and

the facets size on the global properties of the fabricated panels. For fabricating the designed

origami panels, fused deposition modeling was utilized, and the material filament used was PLA,

provided by Spool Works, with a diameter of 1.75 mm. The fabrication conditions were set as

following: the extruder temperature 240 C, the layer height 0.20 mm, the infill 25%, and the

number of shells 2. Compression and impact tests were also conducted on the fabricated samples

and then characterized for compression and impact loads. The designed models were also

simulated for compression and impact properties using ANSYS finite element package. In

addition to the passive properties, the unit elements were also tested for shape memory effect.

Chapter 6 is on modeling origami structure using representative unit cell (RUC). The modeling is

intended to predict the mechanical response of the origami metamaterials. As part of the

modeling, a representative unit cell (RUC) was developed to predict the mechanical properties of

origami structures. The viscoelastic properties of the parent material at elevated temperatures

were included in the model. The actual skeleton of the origami structure should be representative

in order to capture the mechanics of deformation, to predict the overall mechanical properties

and behavior. Shell theories are suitable for modeling the origami structure since all individual

segments are thin or moderately thick compared to each cell size. The modeling was carried out

with the commercial finite element package ABAQUS. Thick shell elements adopted for the

analysis. This element is applicable for thick and thin shell applications for permitting large

strains. This shell element allows for the analysis of buckling and warping of individual surfaces

of the origami structure. Displacement-based periodic boundary conditions were assumed to the

edges of the representative unit cell (RUC) as appropriate. The periodic boundary conditions are

implemented in the opposite edges of the (RUC) in which the relative displacement between

these edges equal zero,

8

Chapter 7 summarizes the overall thesis work and provides final remarks and the conclusion, in

addition to the recommendation for future directions.

9

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Cohen, Applied origami. Using origami design principles to fold reprogrammable

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Single Vertices to Metasheets, 055503 (2015) 2–6. doi:10.1103/PhysRevLett.114.055503.

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[12] Y. Klett, H.S.Þ. L, P. Middendorf, Kinematic Analysis of Congruent Multilayer

Tessellations, 8 (2018) 1–7. doi:10.1115/1.4032203.

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with folded core under impact load, in: Proc. 8th Int. Conf. Sandw. Struct. ICSS8, Porto,

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11

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by an elastic instability, Adv. Mater. 22 (2010) 361–366. doi:10.1002/adma.200901956.

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modules., United States Pat. 3. (1968) 407,558.

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Effect of Polymers, Polymers (Basel). 6 (2014) 1144–1163. doi:10.3390/polym6041144.

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13

Chapter 2.

Material Selection and Characterization

2.1 Introduction

Selecting the appropriate material is one of the main considerations in the design process of

mechanical parts. The design cannot be carried out without knowing the material properties and

the way the material can be treated to form the specific designed parts [1]. During the material

selection stage, the cost, the manufacturing and forming process, and the physical and

mechanical properties should be taken into account in the design process [1].

Recently, the usage of sandwich structures has gained much interest in different applications.

The aerospace industry faces the necessity to develop high efficiency structures with low density

and cost. The design of sandwich cores requires materials that have low density, high impact

damping properties, and good at corrosion resistance [1-4]. Polymers are materials that have a

wide range of mechanical and physical properties that can be utilized to design mechanical

structures that can serve different applications. They are characterized by low density and low

moduli compared with metals, and they may be the best choice for applications that require low

density materials, they can perform better in dissipating compression and impact loads, but also

they can be strong enough to be used in different applications [1]. The large elastic deflections

of polymers can be utilized to dissipate incoming loads. Furthermore, the combination of

mechanical properties of multi polymers can be used for tailoring the target application design

requirements [1].

This study is devoted to characterize the viscoelastic behavior of polymeric blends made of two

blended polymers with six different weight percentages. The main objective of the study is to

combine the properties of two polymers, to produce material blends with properties that can be

used to fabricate origami structures for compression and impact applications. These two

polymers are Poly-Lactic Acid (PLA) and thermoplastic polyurethane (TPU), in which PLA

considered as a major phase and TPU which considered as filler. Each of these two polymers has

some desirable properties for both compression and impact resistance. Including the two pure

14

polymers of PLA and TPU, the other weight percentages of the PLA/TPU material blends were

80/20, 65/35, 50/50, 20/80. The study investigates the mechanical, the viscoelastic properties

and morphology of the produced polymer blends.

2.2 Material Processing and Characterization

The two selected polymers used for this study are PLA and TPU, they are both easy to process

and they both compatible [5]. The main characteristics of the PLA are, PLA is bio-based

polymer, bio-degradable, recyclable; it needs low energy processability, and good mechanical

properties [6-13]. The other polymer is TPU which is consists of hard and soft segments it is

characterized by toughness, impact resistance, and strength. Both segments are able to melt to

form thermoplastics [14-19].

PLA of grade (3052D) was bought from Natureworks LLC (USA), and TPU of grade (55D) was

obtained from Lubrizol Engineering Polymers (USA). Both polymers were in pellet form, and

the melting temperatures as reported were 160 °C for PLA and 181 °C for TPU. Each of these

Polymers has its own limitations that limit them to be used in some applications, and therefore

they need to be enhanced by adding other fillers or combining them with another polymer to

produce new polymeric blends. PLA has some limitations in some properties such as toughness,

impact strength [20,21]. The blends properties will depend on the blend composition; PLA is

selected to improve the strength of the blends, which is one of the major required properties of

sandwich cores, while the TPU is utilized to enhance the impact properties of the blends. The

weight percentages were selected based on previous studies in which some of these blends

combinations exhibited superior mechanical properties [22].

To melt and compound the two polymers a twin screw micro-compounder model (MICRO15,

DSM; Geleen, Netherlands) was used. The PLA – TPU weight percentages in the produced

blends were (80/20, 65/35, 50/50, 20/80, and the pure PLA and TPU). The blends were carried

out by first mixing the two polymers pellets and feeding the micro-compounder to melt the

mixture, for about 10 minutes with a rotor speed on the compounder screws of 30 rpm, and then

the mixed blend extruded out of the compounder forming straight strips, those strips were

pelletized to ensure uniform distribution of the material. A schematic of the process is illustrated

in figure 2.1. Figure 2.2 shows the comparison of density change of the material blends.

15

Figure ‎0.1 Schematic of compounding process used to produce material blends

Figure ‎0.2 Comparison of the density of the material blends

16

2.3 Experimental Work

2.3.1 Material Blending Morphology

Scanning electron microscopy SEM was used to investigate the miscibility of the two polymers

phases. The samples were fractured using liquid nitrogen and then coated using a gold coating to

better visualize the two polymers phases using the SEM. After coating the samples, SEM (FEI

quanta 250) was used to view the morphology of the material blends samples.

2.3.2 Differential Scanning Calorimetry (DSC) Test

The differential scanning calorimetry (DSC) test has been conducted for the polymeric blends

using DSC Q2000 from TA. Small samples were prepared of masses rage of (10 – 12mg). The

test conducted by running heat/cool/heat cycles for a temperature range from -70 C to 200 C,

and the temperature rate set at 10 C/min. The temperature features of the tested samples were

concluded from the test.

2.3.3 Dynamical Mechanical Analysis (DMA) Test

To characterize the viscoelastic behavior of the material blends, Dynamical Mechanical Analysis

DMA test was conducted, to obtain the storage modulus and loss modulus for the material

blends. To perform the test, rectangular samples were prepared by injection molding and the

size of the sample was 12x60 mm. DMA Q800 from TA was used for this test. The temperature

range set from 25C to 80C, with a fixed temperature rate of 5 C/min. And the test mode used

was a dual cantilever.

2.3.4 Rheological Test

The rheological test was conducted using TA-ARES. Three samples from each material blend

were prepared and tested. The sample was in a disc shape with a diameter of 25mm and 1.5mm

thickness. The samples were prepared using compression molding process, in which the material

blends uniformly spread in the disc mold space and kept in temperature just above the melting

temperature of the blends, and then a 3-ton pressure was applied for 10 minutes. The storage,

loss modulus, and viscosity were recorded form the test. The test temperature was 190C.

17

2.4 Results and Discussion

2.4.1 SEM Morphology of Blended Polymers

To observe the dispersion of TPU and PLA, The SEM imaging was carried out. Figure 2.3 shows

the SEM images of PLA/TPU blends composition including the pure PLA and TPU. Neat PLA

showed a smooth surface, as we can see in figure 2.3a. The increasing of the TPU content in the

blends showing some regions with a different color due to the two segments that TPU composed

of. PLA and TPU are compatible polymers and they create immiscible phases, as shown in figure

2.3 b, c, d, and f. This is consistent with the results of previously published research done on

visualizing the morphology of PLA/TPU [23-26]. Figure 2.3 f, showing the micrograph of the

neat TPU.

Figure ‎0.3 SEM morphology of blended polymers, PLA/TPU wt %. a) 100/0, b) 80/20, c) 65/35,

d) 50/50, e) 20/80, and f) 0/100.

2.4.2 DSC Test Results

The thermal behavior of the material blends was determined using DSC, and the samples were

subjected to a cool/heat/cool cycle, in which the glass transition, melting and the crystallization

temperature can be concluded. The samples were cooled up to -55 C and then heated to about

195 C with a constant heating rate. The results of the six blended compositions were illustrated

18

in figure 2.4. Based on the TPU hard and soft segments glass transition temperature two peaks

can be observed in glass transition behavior, and it did not vary much the compounded blends.

Figure ‎0.4 DSC Thermosgrams for PLA/TPU wt % blends.

2.4.3 DMA Test Results

The Dynamic mechanical analyzer was used to predict the viscoelastic properties of the blended

polymers. The results of the test are illustrated in figure 2.5 and 2.6. The figures show the

changing in the storage and loss moduli based on material blends composition. The values of the

storage modulus tended to decrease by the increase of the TPU content and it began at more than

3000 MPa. It is observed that both storage and loss moduli for the samples of material blends

contain 50% PLA and more behave similar to pure PLA samples, and the ones with TPU more

than 50 % followed the same behavior of pure TPU sample.

19

Figure ‎0.5 Comparison of the storage modules of the polymers blends.

Figure ‎0.6 Comparison of the loss modules of the polymers blends.

2.4.4 Rheological Properties

The PLA/TPU blends and the pure polymers were tested for viscoelastic properties; the test was

conducted under the following conditions: the temperature kept at 190 °C, the frequency sweep

rage was 10 – 500 rad /sec and the shear strain was 5%. The results of the test of the six tested

samples are illustrated in figures 2.7-2.9. The results show the storage (G) and loss (G) moduli,

20

in addition to the complex viscosity (). Those moduli are important to measure the stored and

the dissipated energy for a viscoelastic material. The curves show that the PLA has the lowest in

values of (G) and (G), while the 50/50 sample showed the highest values of storage and loss

moduli followed by 65/35 and 20/80, and the 80/20 lied between the TPU and PLA samples. The

complex viscosity behavior also followed the same trend of the storage and loss moduli.

Figure ‎0.7 Rheological properties of PLA/TPU wt % blends (storage modulus).

Figure ‎0.8 Rheological properties of PLA/TPU wt % blends (loss modulus).

21

Figure ‎0.9 Rheological properties of PLA/TPU wt % blends (complex viscosity).

2.5 Conclusion

To improve the mechanical properties of one polymer there are many procedures used. One of

the effective ways is to compound two polymers to combine the properties of the two polymers.

Two polymers (PLA and TPU) were selected to produce polymers blends of different weight

percentages. The blends were produced by using twin screw compounder. The structure, thermal

properties, and the viscoelastic properties of the produced blends were studied. PLA and TPU are

immiscible polymers but they are able to create compatible blends. The DSC tests showed the

effect of the increase of the soft material TPU in the glass transition temperatures of the tested

blends. The DMA results showed that by the increase of the TPU content, the storage and loss

modules decrease. The rheological properties were studied and the storage, loss and complex

viscosity were concluded.

22

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of electrospun ethylene vinyl alcohol copolymer ( EVOH ) fi bres on the structure , morphology ,

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domains in PLA through star-structured polylactides with dual plasticizer / nucleating agent

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Fabrication and characterization of a foamed polylactic acid (PLA)/ thermoplastic polyurethane

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25

Chapter 3.

Development and Modeling of Multi-phase Polymeric Origami Inspired Architecture by Using Pre-molded Geometrical Features1

Using Origami folded cores in sandwich structures for lightweight applications has attracted

attention in different engineering applications, especially in the applications where the stiffness

to weight ratio is a critical design parameter. Recently, common sandwich cores such as honey-

comb and foamed cores have been replaced with origami core panels due to their way of force

redistribution and energy absorption; these unique characteristics give origami cores high

stiffness to weight ratio and high bending and twisting resistance. This work presents the results

of experimental investigations of the effect of base material on the mechanical properties and the

impact resistance of Miura-Origami sandwich cores; then, the experimental results are compared

with FEA simulation results. The materials used in the study for the origami cores were polymer

blends composed of polylactic acid (PLA) and thermoplastic polyurethane (TPU). PLA/TPU

blend compositions are (100/0, 80/20, 65/35, 50/50, 20/80, and 0/100) as a weight percentage.

The geometrical parameters of the unit cell, base material thickness, and the panel thickness were

considered to be constants in this study. The study shows the behavior of the origami cores under

impact test and the energy absorbed by the origami folded cores. It was found that 20/80

PLA/TPU blend demonstrated the highest specific energy absorption efficiency both in quasi-

static compression and impact tests. Fractured Origami structures were observed to fail at folded

edges (creases lines), while the facets exhibit rigid body rotations. The FEM simulation showed a

consistency in the impact behavior of the origami cores, and the directional deformational of

origami core units which explain the ability of the structure to redistribute the applied force and

1 The content of this chapter has been published in the Journal of Smart Material and Structures;

Kshad M A E and Naguib H E 2016 Development and modeling of multi-phase polymeric origami inspired

architecture by using pre-molded geometrical features Smart Mater. Struct. 26 (2017) 025012 (10pp)

DOI:10.1088/1361-665X/26/2/025012

26

absorb energy. In this work the origami folded core features were molded directly from the

blended material.

3.1 Introduction

Sandwich core structures, usually composed of a thick lightweight core covered by two thin and

stiff faces [1], are widely used for energy-absorption applications. Conventional sandwich core

structures with honey-comb, foam, and ribbed stiffened cores have been used for such

applications for many years. The mechanical performance of honeycomb cores deteriorates over

time due to the moisture accumulation inside the sealed cells [1,2]. Recently, many new types of

core structures have evolved for lightweight structures, such as truss core panels, open and

closed cell foamed cores, functionally graded foams, and folded cores [3]. The global mechanical

properties of two dimensional sheets can be enhanced by introducing a local texture to the

material sheet [4]. The new manufacturing methods have allowed folded cores to be more

promising for such applications [3]. Origami is the art of paper folding in which complex spatial

objects can be created from a flat sheet [5]. It has an intrinsic source of inspiration for innovation

of mechanical metamaterials, for which the material properties are defined more by the geometry

and the way the materials are arranged than from the properties of its parent materials [5,6].

Rigid origami, in which the faces between the crease lines remain rigid and only the creases

deform during the folding process, has an advantage over other classes of origami patterns that

require faces bending and crumbling. During the load application, only crease lines deform while

the faces have rigid body rotation [7]. Most previous studies have focused on periodic origami

patterns; however, the non-periodic origami patterns have not yet received attention because of

their complexity in theoretical modeling [7,8]. The main idea behind origami folded cores is their

ability to absorb impact and compression energy through deformation of tessellation patterns,

which is due to the collapse mechanism of the tessellation faces along folding lines without

causing material rupture [4]. The origami pattern of origami tessellation is periodic in the planar

direction, and the unit cell geometry, which consists of four identical faces joined through the

crease‎ lines,‎ is‎ characterized‎ by‎ the‎ faces’‎ dimensions‎ and‎ folding‎ angles.‎ The‎ mechanical‎

properties of the origami cores are characterized in a partly folded state [7,9]. The geometrical

mechanics and characteristics of origami patterns have been studied by many researchers [7,9].

27

Furthermore, many research studies have provided mathematical and analytical models for the

origami folded cores, including computer simulations and finite element analysis [5,7]. Extensive

work has been carried out in the progress and development of folded cores in Tupolev State

Technical University [10–14], in which different folded cores with different folding patterns

have been investigated for mechanical properties and engineering applications [3]. Alekseev [15]

has presented a simulation of geometrical parameters of both regular and irregular folded cores

using CAD systems for designing the structure. A theoretical and experimental study to

determine the characteristics of Z-Crimp cores has been introduced by Paimushin, et al. [15],

while Shabalin et al. [16] provided a simulation of Z-Crimp shaping using the ANSYS finite

element package. The effect of the geometrical parameters of Z-Crimp origami pattern on

strength under transverse compression and longitudinal shear at the same volumetric density

made of different materials has been investigated by Dvoeglazov et al. [17]; the authors outlined

valuable recommendations for the selection of structural parameters concerning origami

structures for high strength. Tolman et al. [18] have introduced a three-stage strategy for material

selection of Miura-origami structure. A numerical investigation of Miura-origami cores under

quasi-static loads has been done by Zhou et al. [1], in which they found that the performance in

compression and shear of the models with curved lines higher than the flat faced origami cores.

The objective of this study is to introduce an experimental investigation supported by finite

element evaluation of the effect of base material on the mechanical properties and the impact

resistance of Miura-Origami cores. The origami structures were geometrically molded at the

fabrication stage without post folding of flat sheets. The materials used in the study for the

origami cores are polymer blends composed of polylactic acid (PLA) and thermoplastic

polyurethane (TPU). PLA/TPU blend compositions are (100/0, 80/20, 65/35, 50/50, 20/80, and

0/100) as a weight percentage. The origami pattern is periodic in the planar direction, and the

unit cell geometry is characterized by four identical faces and folding angles. The mechanical

properties of the origami cores are characterized in a partly folded state. The geometrical

parameters of the unit cell, base material thickness, and the panel thickness are considered

constants in this study. The study presents the results of the compression test, the impact

resistance, and the energy absorbed by the folded cores in the impact test. The finite element

simulation has been conducted by modeling the origami structure as a sandwich, using the

28

explicit dynamics solver provided by ANSYS software, the shell element type used to represent

the origami cores and the sandwich faces, the impactor modeled as a rigid part.


3.2.1 Materials Processing

The materials used to produce polymeric blends for origami samples are Poly-Lactic Acid (PLA)

(3052D) obtained from Natureworks LLC (USA), the reported melting temperature range of

PLA is 145 – 160 °C and the density is 1.24 g/cm3. PLA is a bio-based polymer has advantage

mechanical properties, low energy processability, and it is also bio-degradable [19]. The main

drawbacks of PLA are its high brittleness, low impact strength and toughness [19]. There have

been a number of studies to improve these limitations; one of the effective ways is to form PLA

blends with other polymers like Thermoplastic polyurethane (TPU) which features by strength,

ductility, impact resistance and toughness [19]. TPU is grade (55D) obtained from Lubrizol

Engineering Polymers (USA). The reported melting temperature of TPU is 181 °C and the

density is 1.16 g/cm3. Both polymers are in pellet form, the weight percentage of PLA/TPU

blend compositions used were 80/20, 65/35, 50/50, 20/80, in addition to the neat PLA and TPU.

A twin screw micro-compounder (DSM; Geleen, Netherlands) (MICRO15) was used to fabricate

the material blends, by melting and mixing the pellets at a temperature range of (185 – 195 C)

with the screw speed of 30 rpm for 10 min. Then, the blends were extruded and pelletized.

3.2.2 Fabrication of Origami Structures

Three samples from each batch have been fabricated using compression molding. The mold was

designed in three parts, allowing the samples to be removed easily after molding (see figure 3.1-

a). The molding temperature was kept at 205 C and pressure of 3 Tons. Silicon based mold

release spray was used to help releasing the samples from the mold. During the first samples

preparation, a lot of bubbles were observed in the produced samples, so the mold has been sealed

using fiber reinforced rubber to prevent bubbles occurrence and to avoid polymer leak. The

pelletized material blends were melted and compressed between the upper and lower jaws of the

29

mold and then held at 3 Tons for 10 minutes to allow uniform distribution of the material.

Tensile specimens were also prepared for tensile test from each blend according to ASTM 638.

Figure ‎0.1 a) Multi-stage compression mold used to fabricate origami cores b) The geometrical

parameters of fabricated origami cores.

3.2.3 Miura Origami Unit Cell and Core Configuration

Origami structure consists of a periodic tessellation of unit cells, which are made of thin-walled

faces connected at fold lines; it gains its unconventional mechanical properties from the

interaction between the fold lines and the deformation of the interlaying faces [4]. Periodic

origami geometry is defined by a repetitive unit cell, characterized by specific geometric

parameters. Figure 3.1-b shows the panel of Miura-origami in partially folded state. The unit cell

can‎be‎characterized‎by‎a‎specified‎set‎of‎its‎face’s‎parallelogram‎independent‎parameters‎and‎the‎

folding angle. The pattern parameters can be calculated using equations (1-4) [8,10]:

, (1)

, (2)

, (3)

(4)

30

where H, a and b, , , S, L, and V are the height of the origami panel, the face dimensions of

the unit cell, parallelogram angle, fold angle, surface area, unit cell height, and the overall

volume, respectively [8,10]. The folded core panel is defined by the number of tessellations,

which is defined by the size of the core panel (W, L, H) where W, L, and H are the width, length,

and height of the core panel, respectively. The geometrical parameters used to generate the

origami core samples are (a = b = 24 mm, W = L = 120 mm, H = 20 mm, = = 45 , and the

thickness is 1.5 mm).

The volumetric density of the origami panel can be calculated using equation (5),

(5)

where c is core volumetric density, t is parent material thickness, and m is parent

material density [8,10]. Table 3.1 shows the values of blended materials densities and the

origami core volumetric densities made from PLA/TPU blends.

Table ‎0.1 Material blends density and origami volumetric density.

Material Blends (PLA/TPU)

wt %

Material Blends Density

(g/cm3)

Volumetric Origami Density

(g/cm3)

Neat PLA 1.24 0.161

80/20 1.220 0.158

65/35 1.213 0.157

50/50 1.198 0.155

20/80 1.175 0.152

Neat TPU 1.16 0.150

3.2.4 Compression Test

A compression test, which measures the capacity of origami cores to withstand compressive

loads, was conducted to determine the strength of origami cores which. The origami core

31

samples were tested using a compression testing general machine. Two thick steel plates have

been assembled with the testing machine allowing the load to be uniformly distributed on the

origami panel structure. The test was consistent with ASTM D1621/94 standard with 5 mm/min

stroke. Three specimens were tested for each origami structure. Each sample has 9 periodical

cells (see figure 3.1-b) with a cell size of (40*40 mm). A tensile test of base materials was

conducted according to ASTM D638 standard to determine the tensile modulus.

3.2.5 Impact Test

Impact test conducted using a custom setup which was designed to measure the force and the

energy transferred by the tested sample due to impact event. The origami core is sandwiched

between two flat polycarbonate sheets with a thickness of (7 mm) (figure 3.2-a). Then the

sandwich samples were placed on the flat disk of the test stand which is connected to a quartz

based dynamic load sensor (Dytran, 1060V) see figure 3.2-b. By adjusting the dropped weight

we vary the impact energy; in this study the impact weight is 1.104 kg while the drop height is

66.5 cm. The test was conducted based on ASTM D7136/D7136M standard. Force and time

were recorded during the impact event.

Figure 3.2. a) Origami Sandwich core sample, b) Sandwich sample placed in the test stand.

32

3.3 Simulation and Analysis

3.3.1 Compression Simulation

In order to simulate the compression tests, the Static Structural analyzer provided by ANSYS

was used. In the simulation, the origami core placed on a thick steel plate, and it was represented

by shell elements, and the thick plate was represented by solid elements. Frictions-less contacts

between the origami core and the plate have been defined, and the lower side of the plate was

constrained by fixed boundary condition. A compression strain of 10.1 mm was applied as a

compression load. Figure 3.3-a shows the meshed geometry of the compression model.

3.3.2 Impact Event Simulation

For impact event simulation, the explicit dynamics solver provided by ANSYS was used: the

origami core and sandwich faces were represented by shell elements, while the impactor was

represented by solid elements. Fixed boundary condition was used in the bottom side of the

lower plate, and free directional constraints were used for the impactor in the load direction.

Frictionless contact has been defined between the impactor and the upper side of the upper plate

of the sandwich, and bonded contacts between the sandwich faces and the origami core have

been defined. Figure 3.3-b shows the meshed geometry of the origami sandwich structure. The

mass of the impactor used to be 1.1014 kg and the contact velocity was 3571.137 mm s-1. The

impact event end time was 0.002 s.

33

Figure ‎0.2 The meshed geometry of the origami a) compression simulation, b) impact

simulation.


3.4.1 Compression Test Results

The compression test of the origami cores shows that with the increase of the soft material

(TPU), the origami core strength decreases while the origami core samples with high content of

PLA have the higher strength. In contrast, samples with high percentages of TPU have higher

compressive strains. Samples with high strength values experienced fracture along the crease

lines, while high TPU content core samples were able to recover, but at the expense of the

strength. Figure 3.4 shows the stress-strain behavior of the origami cores, and figure 3.5 shows

the changing in elasticity modulus and the strength of the origami cores, respectively. Figure 3.6

compares the compressive deflection behavior at maximum stress and the maximum stress of the

origami cores. The toughness of the origami cores illustrated in figure 3.7, PLA samples have the

maximum values of toughness of about 1500 (J/m3), this value keeps decreasing by the increase

of TPU amount to about 600 (J/m3) for 50/50 (PLA/TPU) sample, and to about 210 (J/m3) for

the neat TPU samples. By the controlling the material blends weight percentage; it is possible to

tailor the compression stiffness and strength.

34

Figure ‎0.3 Compression stress-strain relation of origami core structure.

Figure ‎0.4 . Modulus of elasticity and strength of origami cores.

Figure ‎0.5 Comparison of maximum stress of origami cores and the deflection at maximum

stress.

35

Figure ‎0.6 Comparison‎of‎origami‎cores’‎toughness.

Compared with the specific modulus of elasticity of blended material, origami cores show low

modulus values. Table 3.2 shows the comparison value of the specific modulus of elasticity. The

values of origami strength are comparable with the honeycomb cores made of aramid fiber sheet

(HRH10-3.2-144) [20], have the same density rage (144 Kg/m3 10%) (6.5 MPa) and the

origami strength ranges between (4.6 ~ 0.5 MPa).

Table ‎0.2 Comparison of specific modulus of elasticity of solid blended material and origami

cores.

Material Composition

(PLA/TPU) w%

E, of solid material blend

(MPa.m3/Kg)

E, of origami cores

(MPa.m3/Kg)

100/0 (PLA/TPU) w% 831.9 28.6

80/20 (PLA/TPU) w% 710.6 21.2

65/35 (PLA/TPU) w% 651.9 17.7

50/50 (PLA/TPU) w% 646.4 12.5

20/80 (PLA/TPU) w% 208.1 7.7

36

0/100 (PLA/TPU) w% 29.6 3.4

Figures 3.8 and 3.9 show the SEM images of fractured cores along crease lines for neat PLA and

80/20 PLA/TPU origami cores. PLA exhibits brittle-like fracture surface while the 80/20

PLA/TPU core shows cup-cone fracture surface that can be considered as ductile failure. This

result illustrates brittle to ductile transition with more percentage of TPU added to PLA for the

origami core structures. This is important when designing origami structures where a balance

between the brittleness and ductility in the material controls the compressive strength and energy

dissipation, respectively. Increasing the brittle content (PLA) enhances compressive strength

while the ductile content (TPU) promotes energy dissipation through plastic or large

deformation.

Figure ‎0.7 SEM images of fracture surface of Neat PLA origami core with magnification a)

40X, b) 130X, c) 750X.

Figure ‎0.8 SEM images of fracture surface of 80/20 PLA/TPU origami core with magnification

a) 40X, b) 130X, c) 750X.

37

3.4.2 Impact Test Results

In order to characterize origami structure during impact event, the procedure developed by

Joshua‎has‎been‎adopted‎in‎our‎analysis‎[10].‎Newton’s‎second‎law‎is‎used‎and‎the‎solution‎for‎

acceleration, a(t), is given as:

(6)

where g is the gravitational acceleration constant, P(t) is the load with respect to time, and M is

the mass of the impactor. Zero time is considered when the impactor strikes the origami

sandwich, so the following can be defined

(7)

where V is the velocity just prior to impact.

Integrating equation (9) to obtain expression for v(t) yields

(8)

Once the previous quantities are obtained from our experimental setup, solving for the energy

transferred as a function of time gives

(9)

Figure 3.10 shows a sample of transferred impact force by neat PLA origami sandwich structure.

There is force increase at the beginning of impact until a maximum value is reached, and then a

decrease while the origami sandwich structure bounces back the impactor. This curve represents

the‎P(t)‎values‎in‎the‎equations‎above.‎V‎is‎calculated‎from‎Newton’s‎equation‎of‎falling‎objects‎

for an impactor mass of 1.104 Kg and drop height of 66.5 cm which reveals a value of 3.571134

m/sec. Maximum force and energy transfer is observed at high percentages of PLA which is

attributed to the high compressive resistance due to brittle nature. The 20/80 PLA/TPU blend

transfers force of 1.88 KN which is the lowest for all origami sandwich structures (see figures

3.11 and 3.12). As discussed in the previous section, the selection of the origami material

38

depends on the application where the different percentages of PLA and TPU influence the

amount of force and energy transfer. The reported values in this study are for the transferred

force and energy where the receiver is our primary concern. Neat TPU provides low force

transfer but it has the lowest compressive strength as noted in section 4.1. PLA can be added to

enhance compressive strength while observing the transferred force, see figure 3.12. For

example, 65/35 PLA/TPU blend increases the force transfer from 2.19 KN for neat TPU to 2.8

KN while also increasing the compressive modulus from 0.511 MPa to 2.79 MPa. So as

discussed before, the origami structures can be designed for energy absorption while maintaining

a required strength by controlling the amounts of PLA and TPU.

Figure ‎0.9 Sample of impact force for neat PLA.

Figure ‎0.10 Maximum transferred impact force.

39

Figure ‎0.11 Maximum impact energy transferred.

When compared with conventional materials, origami cores show better impact force damping.

Table 3.3 shows the comparison of the transferred force of (PLA/TPU) origami cores with

polycarbonate and steel sheets during the same impact event.

Table ‎0.3 Comparison of maximum impact force transferred.

Material Maximum Force Transferred (N)

100/0 (PLA/TPU) w% 3708.2

80/20 (PLA/TPU) w% 3085.4

65/35 (PLA/TPU) w% 2806.4

50/50 (PLA/TPU) w% 2584.0

20/80 (PLA/TPU) w% 1882.4

0/100 (PLA/TPU) w% 2195.8

Polycarbonate 11432.9

Steel 20852.0

40

3.4.3 Finite Element Results

The results of the FEM were converging by the decrease of the element size from 1.4mm to 1mm

and then it started diverging (see figure 3.13), the number of shell elements of origami cores was

29198, and the number of nodes was 42514. The static structural analysis of the origami cores

has showed that, the maximum Von-Misses stress was in the neat PLA cores with the value of

853.26MPa, and it keeps decreasing by the increase of the TPU content, which has the minimum

value of 72.946MPa. Figure 3.14 shows the comparison of maximum Von-Misses stress values,

and figure 3.15 shows the Von-Misses stress distribution on the origami cores of neat PLA,

80/20 PLA/TPU, 50/50 PLA/TPU, and neat TPU. It is clear that the high values of stresses occur

in the crease lines, and they become the stress concentration zones, while the faces are the low

stress areas, as a result the facture always expected to happen along the crease lines.

Figure ‎0.12 The change of the results error (%) by changing the mesh size.

41

Figure ‎0.13 Comparison of Von-Misses stress values for origami cores of different material

blends.

Figure ‎0.14 Von-Misses stress distribution on origami cores a) Neat PLA, b) 80/20 PLA/TPU, c)

50/50 PLA/TPU, and d) neat TPU.

The explicit dynamics simulation of the origami sandwich cores has showed the impact behavior

of the origami cores, the total energy, the internal energy, and the reaction force have been

42

demonstrated, see figure 3.16, it is clear that, cores with high percentage of TPU have higher

internal energy than the cores with the high percentage of PLA. The force transferred (reaction

force) was distinctly decreases by the increase of the TPU percentage as illustrated in figure

3.17. The directional deformations along the load direction were high in the cores with high TPU

contents. Cores with 80% TPU have double of the energy value of the 80% PLA cores, and the

reaction force in the outer-side of the lower plate almost equals the half value, as shown in figure

3.13. Origami PLA samples can dissipate energy up to 2.6 J, while the value increases by the

increase of the TPU content, where the maximum energy dissipated was in the 20/80 PLA/TPU

samples with 3.3J, and it was slightly decreased in the neat TPU samples because of the

densification behavior in the soft material (see figures 3.16 and 3.17). Figure 3.18 shows the

directional deformation in the load direction of origami cores made of neat PLA and neat TPU

respectively.

Figure ‎0.15 The total energy, internal core energy, and the energy dissipated by origami cores.

Figure ‎0.16 Reaction force, and the directional deformation.

43

Figure ‎0.17 Directional displacement of origami core a) PLA b) TPU.

3.5 Conclusion

Origami metamaterial can offer many benefits to many engineering applications, most

importantly high stiffness, high energy absorption efficiency, and light-weight. Miura Origami

structures are fabricated in this work by direct molding of the geometrical features from PLA and

TPU polymeric blends. Direct molding avoids the defects related to a conventional folding of flat

sheets when typically making origami structures. The following blends were fabricated for

PLA/TPU (100/0, 80/20, 65/35, 50/50, 20/80, and 0/100). Those different percentages of PLA

and TPU reflect the increase in compressive strength or energy transfer respectively. The balance

between PLA and TPU will depend on the intended application. PLA origami structure offers

maximum force transfer of 686.1 N and highest compressive modulus of 4.6 MPa. The high

compressive modulus of PLA resulted in fracture at crease lines. The high modulus of PLA

origami structure can be reduced to 2.79 MPa by adding 35% of TPU which offers more

elasticity and avoid failure at high compressive strains. The addition of 35% TPU also reduces

the force transfer to 2.8 KN. The finite element modeling has been conducted using static

structural for compression test and explicit dynamics for impact event. The compression results

showed that the crease lines are the stress concentration zones, and it is subjected to fracture in

the blends with high elastic modulus while the faces carry low-stress values. The FEA results

also demonstrated that origami made structure made of a high percentage of 80% TPU has the

44

highest values of energy absorption (up to 3.3 J), with directional deformation exceeded (1.6

mm), and it has the lowest Von-Misses stress in compression. This work provided numerical

quantification of the compromise between compressive strength and energy transfer which can

be used to design origami structure with target values for both.

45

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[13] Kayumov R a., Zakirov I M, Alekseev K P, Alekseev K a. and Zinnurov R a. 2007 Determination of

load-carrying capacity in panels with chevron-type cores Russ. Aeronaut. (Iz VUZ) 50 357–61

[14] Khaliulin V I and Inkin V A 2013 Calculation of process variables at composite Z-crimp shaping

using the folding method Russ. Aeronaut. (Iz VUZ) 55 417–23

[15] Paimushin V N, Zakirov I M and Karpikov Y A 2013 Theoretical and experimental technique of

determining the mechanical characteristics of folded structure filler in the form of Z-crimp (shear

of a filler in cross-sectional planes) Russ. Aeronaut. (Iz VUZ) 56 234–46

[16] Shabalin L P, Sidorov I N and Khaliulin V I 2010 Simulation of Z -Crimp Shaping with the Use of

the ANSYS Finite Element Software 53 339–44

[17] Dvoeglazov I V and Khaliulin V I 2013 A Study of Z-Crimp Structural Parameters Impact on

Strength under Transverse Compression and Longitudinal Shear Russ. Aeronaut. 56 15–21

[18] Tolman S S, Delimont I L, Howell L L and Fullwood D T 2014 Material selection for elastic energy

absorption in origami-inspired compliant corrugations Smart Mater. Struct. 23 094010

[19] Jie Ren 2013 Biodegradable Poly lactic acid Synthesis, Modification, Processing and Applications

vol 53 (Shanghai, China: Springer)

[20] HexWeb 2015 ‘HexWeb ® HRH-10,’ HexWeb ‘HexWeb® Nonmetallic Flex-Core’, [Online].

Available: http://hexcel.com/Resources/DataSheets/Honeycomb-Data-Sheets/HRH_10_eu.pdf

(Accessed: 27 October 2016)

47

Chapter 4.

Carbon Nano Fibers Reinforced Composites Origami Inspired Mechanical Metamaterials with Passive and Active Properties2

Core panels used for compression or impact damping are designed to dissipate energy and to

reduce the transferred force and energy. They are designed to have high strain and deformation

with low density. The geometrical configuration of such cores plays a significant role in

redistributing the applied forces to dampen the compression and impact energy. Origami

structures are renowned for affording large macroscopic deformation which can be employed for

force redistribution and energy damping. The material selection for the fabrication of origami

structures affects the core capacity to withstand compression and impact loads.

Polymers are characterized by their high compression and impact resistance; the drawback of

polymers is the low stiffness and elastic moduli compared with metallic materials. This work is

focused on the study of the effect of Carbon Nano Fibers (CNF) on the global mechanical

properties of the origami panel cores made of polymeric blends. The base matrix materials used

were Polylactic Acid (PLA) and Thermoplastic Polyurethane (TPU) blends, and the percentages

of the PLA/TPU were 100/0, 20/80, 65/35, 50/50, 20/80, and 0/100 as a percentage of weight.

The weight percentages of CNF added to the polymeric blends were 1%, 3%, and 5%. This work

deals with the fabrication process of the polymeric reinforced blends and the origami cores, in

order to predict the best fabrication conditions. The dynamic scanning calorimetry and the

dynamic mechanical analyzer were used to test the reinforced blended base material for

thermomechanical and viscoelastic properties.

2The content of this chapter has been published in the Journal of Smart Material and Structures;

Kshad,‎M.A.E.,‎D’Hondt,‎C.‎and‎Naguib,‎H.E.,‎2017.‎Carbon‎nano‎ fibers‎ reinforced‎composites‎ origami‎inspired‎

mechanical metamaterials with passive and active properties. Smart Materials and Structures, 26(10), p.105039.

https://doi.org/10.1088/1361-665X/aa8832

48

The origami core samples were fabricated using per-molded geometrical features and then tested

for compression and impact properties. The results of the study were compared with previous

published results which showed that there is considerable enhancement in the mechanical

properties of the origami cores compared with the pure blended polymeric origami cores. The

active properties of the origami unit cell made of composite polymers containing a low

percentage of CNF were also investigated in this study, in which the shape memory effect test

conducted on the origami unit cell.

4.1 Introduction

Presently, mechanical metamaterials; materials that gain their properties from their structure

rather than from the base material composition, have received increasing interest in research due

to their superior properties that can be exploited for designing novel materials with high-end

functionalities composition [1-3]. These materials have enormous potential use for sandwich and

lightweight structures in aerospace industry and other applications, because of their attractive

properties‎ such‎ as‎ negative‎ Poisson’s‎ ratio‎ (i.e.‎ auxetic‎ materials),‎ negative‎ compressibility,‎

vanishing shear modulus, etc. [1–3]. Origami-inspired metamaterials are auxetic meta-materials,

in which the material is arranged in certain patterns creating 3D-tessellation. These auxetic

properties have enabled the design of new structural materials with superior properties based on

the arrangement of the structural elements [4–6]. Origami based metamaterials, inspired by the

Art of folding papers, have received particular interest for engineering applications, such as

foldable solar panels, medical stents, and sandwich core applications [7,8]. The design of the

pattern of the origami tessellations affects the auxetic properties of the resultant 3D cores [2].

Indeed, the creation of rigidly folded 3D geometric tessellations from 2D sheets, in which, rigid

faces joined by hinges, shows a great promise for those applications by offering good mechanical

properties for low-weight and low amount of used material [9,10].

Apart from these geometric tessellations is the Miura origami structure, which was first

presented by Miura in the 1970s for sandwich core applications and solar panel deployment in

space [7,8]. Miura origami is one of the origami patterns that attracted attention due to its

geometric simplicity, its wide range of possible configurations, and its intriguing mechanical

properties, which lead to great elastic energy absorption and force redistribution. [7, 8, 11, 12].

49

The mechanical properties of fold core structures and origami cores have got wide attention in

the literature, Kayumov et al. [13] introduced a mathematical model to describe the behavior of

chevron type sandwich panel cores. The study of the impact of Z-crimp structure parameters on

the strength under different loading conditions were investigated in [14], Xiang Zhou et. al.

studied the mechanical properties of Miura folded cores. Heimbs et al. [15] investigated the

behavior of the sandwich made of textile-reinforced composite. Based on Miura origami pattern,

You et al.[16] examined morphing sandwich mechanisms. Numerous of research has been done

in the investigating the mathematical and geometrical parameters of foldable core structures [17–

20]. Active origami structures also get interest in the resent years, in which active materials can

be employed for folding and unfolding process [21–24].

The aim of this study is to investigate the effect of CNF on the mechanical properties of origami

structures made of multiphase polymeric blends by using pre-molded process. The material

blends used were PLA and TPU, the weight percentages of the compositions used were 100/0,

20/80, 65/35, 50/50, 20/80, and 0/100, and the reinforcement weight percentages of CNF were

1%, 3%, and 5%. The polymeric blends were compounded with the CNF, and then the

compounded compositions were used for fabricating the origami structures, by using

compression molding.

The compression test was conducted for the fabricated cores to measure the compression and the

strength moduli of the origami cores; also, a drop mass impact test was performed to predict the

transferred force and the damped energy by the origami cores. The results demonstrated that the

compression moduli increased as a result of the increase in the CNF content; these values

showed that there is large enhancement in the moduli of compression and strength of the

composite origami cores, compared with the cores made of pure blends; while the amount of

damped energy during the impact event was reduced by the increase in the CNF percentage.

The folding/unfolding operation of origami structure is important in some origami-based

applications to be externally produced [21]. At very small, large and in remote applications, self-

folding origami made of active materials that convert various forms of energy to mechanical

work, have proven their usefulness use in many of these potential applications [25–30]. Shape

memory polymers (SMP) are active materials that have high shape memory recoverability, that

can be employed in many active applications [11,21,25,26,31,32]. This work also includes an

50

investigation of active properties (shape memory effect) of origami unit cell made of composite

polymers. The shape memory effect test showed that there is high recovery ratio in the PLA with

low percentage of CNF samples.


4.2.1 Materials

The goal of the use of the origami cores is to transform kinetic energy into elastic strain energy

through the elastic deformation of the core structure; therefore, the materials used to fabricate the

origami structures are the key to the global mechanical properties of the origami cores, for target

applications. The materials must be compliant to allow for the free motion of the structure. Also,

since the cores‎ should‎ withstand‎ the‎ bending‎ loading,‎ the‎ material‎ must‎ allow‎ the‎ faces’‎

connections to deform elastically, while also providing enough stiffness in the panels to resist

bending. Therefore, two polymers were selected to produce the material blends which are used as

a matrix reinforced with Carbon Nano-Fibers (CNFs) as a filler to enhance the mechanical

properties of the material blends.

Polylactic Acid (PLA) grade (3052D) was obtained from Natureworks, LLC (USA), and

Thermoplastic polyurethane (TPU) grade (55D) was obtained from Lubrizol Engineering

Polymers (USA).

PLA is a bio-based polymer which has advantageous mechanical properties, is also a bio-

degradable material, which requires low energy processability [33]. PLA is blended with (TPU)

which is characterized by strength, ductility, impact resistance and toughness [34]. Previous

studies showed that both polymers are compatible, and it is easy to compound the two material

phases. Table 4.1, lists the physical properties [28], the tensile test results, and the DSC results of

the base materials used in the experimental work.

The Carbon Nanofibers CNFs used were Pyrograf, PR-19-XT-PS, with an average diameter of

150 nm, which are available in their fiber form or as a master-batch composed of 85% of PLA

and 15% of nanofibers. The use of the master-batch is preferred for safety reasons, but the CNF

fiber form can be manipulated under fume hoods in a designated laboratory with safety

51

equipments. The PLA/TPU weight percentages used are similar to the previous study done for

the pure blends [35], which were (100/0, 80/20, 65/35, 50/50, 20/80, 0/100), and the CNF weight

percentages added to the blends were (1%, 3%, and 5%). A twin screw micro-compounder

(DSM; Geleen, Netherlands) (MICRO15) was used to produce the material blends, by melting

and mixing the pellets at a temperature range of (180 °C – 195°C) with the screw speed of 30

rpm for 10 min; then the blends were extruded and pelletized.

Carbon Nanofibers are fillers used in polymers when multifunctional properties are needed

[36,37]. In our case, the properties that we need to improve are mainly the strength of the

origami cores and the thermal properties (for active properties).

Al-Saleh et al. [38,39] introduced‎multiple‎reviews‎on‎CNF/polymer‎composites’‎properties‎that‎

outline the various improved properties, taking in the consideration the optimal method to

prepare those composites. The fibers need to be well dispersed and distributed in the polymer

matrix to minimize the stress concentration, and to improve the uniformity of the stress

distribution. One important factor is the fiber diameter, which improves the tensile properties due

to a diminution of the number of defects, the contact area between fillers and polymer increases,

as well as the fiber flexibility. The flexibility allows the fibers to keep their aspect ratio

increasing the stress transfer, and enhancing its mechanical properties. It has also been proven

that the CNF increases the complex viscosity, storage modulus and loss modulus of the matrix

polymer. CNF could also change the polymer crystallinity and affect the transition temperatures.

Al-Saleh et al. [38,39] also considered how to blend polymers and CNF by melt-spinning to get a

good dispersion, and to maintain the aspect ratio of the fibers.

Table ‎0.1 The physical, mechanical and the thermal properties used to fabricate origami cores

Material Density (g/cm3) E (MPa) Melting Temperature Tg (C)

PLA 1.24 1060 145 - 160

TPU 1.16 34.0 ~ 181

52

4.2.2 Material Blends Microstructure

Small samples from the composite blends were frozen by using liquid nitrogen and fractured for

imaging the cross section. The samples were prepared and placed on stubs, and then they were

coated with platinum ions using SC7620 Sputter Coater, Polaron, for 3 minutes. The

microstructure images were obtained by using scanning electron microscope micro-scope (JSM-

6060, JEOL) (SEM).

The SEM images of the blended composites are illustrated in figure 4.1, in which figures a, b and

c, show the SEM images of PLA with 1, 3 and 5 wt.% of CNF respectively, it is clear that, the

CNF fibers were homogeneously distributed in the polymeric matrix. Figures 4.1 d, e, and f,

show the SEM images of the 80/20 PLA/TPU with 5 wt.% CNF, 50/50 PLA/TPU with 5 wt.%

CNF, and neat TPU with 5 wt.% CNF, the images show that the CNF were uniformly distributed

in matrix in both 80/20 and 50/50 PLA/TPU composites, while there is slight CNF

agglomeration in the case of neat TPU.

Figure ‎0.1 SEM micrographs of composite blends, magnification factor 20000X, a) PLA with 1

wt% CNF, b) PLA with 3wt% CNF, c) PLA with 5 wt% CNF, d) 80/20 PLA/PTU with 5 wt%

CNF, e) 50/50 PLA/PTU with 5 wt% CNF, f) TPU with 5 wt% CNF.

https://en.wikipedia.org/wiki/Scanning_electron_microscope

53

4.2.3 Fabrication process

To fabricate the origami core structures, a special compression mold was used; the mold was

designed to transfer the geometrical features of the origami structure, to the fabricated cores (see

figure 4.2) [35]. The pelletized material blends were uniformly spread in the mold to ensure the

homogeneous distribution of the material, and to avoid bubbles occurring in the samples; the

mold was initially coated with silicon based mold-release spray, in order to easily remove the

samples. The upper and the lower parts of the mold were set at a temperature of 20C above the

melting temperature of the material blends for 30 minutes, allowing the blended material to melt.

Then, after the upper and lower temperatures were stabilized, the mold was sealed using fiber

reinforced rubber, and was closed without applying pressure for 15 minutes; in this stage, the

melted material flowed through the geometrical features of the origami.

In the next stage, a pressure of (3 - 3.5) tons was applied to the compression mold for 15

minutes; and then finally, the pressure was released and the mold was immersed in a cold-water

bath for the recrystallization process. The melting temperatures of the material blends were

experimentally measured using DSC. Table 4.2 lists the fabrication parameters used for each

material blend. In this process, it was noticed that with the higher amount of CNF the material

blends get more viscous and more material leakage was observed; therefore, thicker sealing

rubber was used to reduce the material leakage. The values of the molding temperatures were

taken to be about 20 °C above the melting range of the composites, because the large mold size

cannot allow the prediction of the temperature of the mold center.

Six samples from each composition were fabricated to be used for compression and impact tests.

Figure 4.2 shows the fabricated origami core sample. For blended material compositions, a dog-

bone shaped samples and rectangular samples were produced according to ASTM 638 and

ASTM D638 standards using injection molding process. Those samples were used for the tensile

testing and the DMA to investigate the mechanical and the dynamic mechanical properties of the

blended compositions.

54

Figure ‎0.2 a) Multi-stage compression mold used to fabricate origami cores, b) Composite

origami structures made by molding process.

4.2.4 Differential Scanning Calorimetry (DSC) Test

Differential scanning calorimetry provided by TA Instruments (Q50 TGA) was used to

characterize‎the‎thermal‎properties‎of‎the‎blended‎materials’‎composition.‎Small‎material‎masses,‎

ranging between 10 - 15g, were cut from each material blend composite and panned in aluminum

pans; the temperature cycle covered the range of -50 C to 180 C, the cooling/heating rate was

10C/min, and heat/cool/heat cycles were conducted to predict the thermal properties of the

tested samples.

4.2.5 Dynamic Mechanical Analysis (DMA) Test

Dynamic mechanical analyzer provided by TA Instruments (DMA Q800) was used to test the

viscoelastic properties of the blended composite materials. The test was carried out on the

rectangular samples prepared by injection molding according to the ASTM D638 standard. A

sinusoidal load with a frequency of 5 Hz is applied under a temperature ramp from 30°C to

85°C. The storage and the loss moduli were measured for each sample.

55

4.2.6 Passive Properties of Composite Origami Cores

4.2.6.1 Compression Test of Composite Origami Cores

To measure the capacity of withstanding the compression loads, the fabricated composite

origami cores were tested in compression, using a compression machine. Three samples from

each composition were prepared and tested. The samples were placed between two thick-rigid

plates connected to the testing machine to ensure the uniform distribution of the compressive

load (figure 4.3). The load was applied gradually at the rate of 5mm/min (ASTM D1621/94

standard), and the load deformation values were recorded; then, the elasticity moduli and the

compressive strength moduli were obtained.

Figure ‎0.3 Composite origami cores placed between thick-rigid plates in the compression test.

4.2.6.2 Impact Test of Composite Origami Cores

For the impact event, a custom drop-weight impact setup was used to measure the impact force

received in the other side of the origami sandwiched cores, during the impact event (figure 4.4).

The test setup has a dynamic load sensor (Dytran, 1060V) placed in the lower side of the testing

plate. This load sensor is connected to the data acquisition system, allowing the recording of the

force-time values of the impact event, and then the force and energy transferred were obtained.

In the test, the impact weight used was 1.104 Kg, and the height was 66.5cm.

56

Figure ‎0.4 Composite origami core sandwiched between two plates, b) Impact test setup.

4.2.7 Active Properties

In order to investigate the active properties of the origami unit cell, the origami core made of

PLA with 0.1% CNF was fabricated, and the unit cell was split for shape test. The shape memory

test started with compressing the origami unit cell using Instron (5848) testing machine, with a

strain rate of 5mm/min as per ASTM D695. The test was done at a temperature of 80 C, which

represents the glass transition temperature of the composite material. Then the relaxation test was

run under the same thermal conditions to remove the residual stresses from the samples, from

which the stress-time relation was recorded. After relaxation test, the deformed origami unit cell

sample was fixed. Finally, the deformed sample was kept under a uniform temperature of 80C,

allowing the origami unit cell geometry to recover; the changing height versus time recorded and

the recovery factor was calculated.


4.3.1 Thermal Properties of Composite Material Blends

4.3.1.1 Differential Scanning Calorimetry (DSC)

Figure 4.5 shows the heat flow curves of the composite blends, which were obtained using DSC.

The curves show the thermal behavior of the material tested. The glass transition temperature

57

range (Tg), and the melting temperatures of the composites were taken from the test, to decide

the fabrication conditions of the composite blends. Table 4.2 lists the values of the Tg, the

melting temperature ranges of blended composites Tm, and the molding temperature ranges used

in the fabrication process.

The DSC results show that the addition of CNF in the base polymer matrix does not significantly

change the glass transition temperature of the TPU, which ranges from -36°C to -31°C or of

PLA, which ranges from 56°C to 60°C. The general behavior is that these temperatures increase

with a higher PLA composition in the PLA/TPU polymer blend, and a higher CNF composition

in the composite.

Table ‎0.2 The DSC Results of the Material blends.

CNF

(w%)

Material Blends Composition

(PLA/TPU) w%

Glass Transition

Temperature Range Tg (C)

Molding Temperature

range (C)

1% 100/0, 80/20,65/35, 50/50, 20/80, 0/100 (-34.55 – 58.65) 210 - 230

3% 100/0, 80/20,65/35, 50/50, 20/80, 0/100 (-32.35 – 59.30) 210 - 220

5% 100/0, 80/20,65/35, 50/50, 20/80, 0/100 (-31.85 – 58.9) 200 - 210

a) Composite blends with 1 w% CNF b) Composite blends with 3 w% CNF

58

c) Composite blends with 5 w% CNF

Figure ‎0.5 Thermal behavior of composite blends with CNF.

4.3.1.2 Dynamic Mechanical Analysis (DMA)

DMA results show the mechanical viscoelastic properties of the composite polymeric blends;

those results are illustrated in figure 4.6, which shows the storage and the loss moduli of the

composite blends. At low temperature, the macromolecules remain stiff, and do not resonate with

the sinusoidal load, while at high temperature; the molecular segments become mobile and then

resonate with the load. By analyzing the curve, we can clearly see the glass transition of PLA

between the energy elastic state and the energy entropy state shown by the sudden drop in

storage modulus and the pronounced peak for loss modulus. The behavior of PLA/TPU blends

shows that, PLA dominates the viscoelastic response up to 50/50 PLA/TPU composition, and

then deviates to TPU behavior. The glass transition of PLA has major consequences on the

viscoelastic properties for high PLA composition up to 50/50 PLA/TPU. Moreover, CNF tends

to increase the storage moduli in a significant way, from 1% to 3% CNF, while the loss moduli

are only slightly improved. From the experiments on 5% CNF, 80/20 PLA/TPU shows

significantly improved moduli, while there seems to be a stagnation starting at 65/35 PLA/TPU

composition and below. For 50/50 PLA/TPU, the DMA results do not show a significant

variation in dynamic moduli, but the 5% CNF loss modulus seems inferior to the 3% CNF. With

59

the actual results for 20/80 PLA/TPU and Neat TPU, there was no significant improvement of

the DMA moduli with the addition of CNF.

a) PLA/TPU Blends with 1% CNF b) PLA/TPU Blends with 1% CNF

c) PLA/TPU Blends with 3% CNF d) PLA/TPU Blends with 3% CNF

e) PLA/TPU Blends with 5% CNF f) PLA/TPU Blends with 5% CNF

Figure ‎0.6 Storage and loss moduli of PLA/TPU blends with CNF.

60

4.3.2 Passive Properties

4.3.2.1 Compression Test Results

The results of the modulus of elasticity of the CNF reinforced blended composite parent

materials are shown in figure 4.7. The compression tests results of the origami composite cores

are shown in figures 4.8 – 4.10, in which figure 4.8 shows a comparison of the modulus of

elasticity values of the composite origami cores. It is clear that, the 5% CNF samples have the

highest values of the elastic modulus in the 20/80, 65/35, and 50/50 PLA/TPU samples, while it

overlaps with the values of 3% CNF in the case of pure PLA, pure TPU and the 20/80 PLA/TPU

samples. The 1% CNF samples always have the lowest modulus.

The strength of composite origami cores is illustrated in figure 4.9, which clearly shows that the

5% samples have the highest strength values compared with the other compositions, similarly to

the behavior of the elastic modulus.

In figure 4.10, the toughness of the origami cores is illustrated, and it is obvious that, samples

with high percentages of CNF absorbed higher energy than the samples with low CNF content,

but with plastic deformation and fracture through the crease lines, as observed in the samples

with high PLA (100% and 80%), while samples with lower PLA percentage showed elastic

behavior during the compression test, and were able to recover after releasing the load.

In general, the elastic modulus and the strength of the composite origami cores decrease in

response to the increase of the TPU composition, which is compatible with the behavior of pure

blended origami results [35]. Samples with high PLA content tend to fracture at the crease lines,

while the samples with high TPU content have the lower elasticity modulus and able to

withstand high strains without fracturing. Comparing these results with previous results of pure

polymeric blends origami [35], it can clearly observe a significant improvement of the strength

and the modulus of the origami cores by the increase of the CNF, Figures 4.8 and 4.9 show

comparison of the compressive modulus of elasticity and the strength of origami cores made of

composite blends and pure blends [35].

61

Figure ‎0.7 Modulus of elasticity of the CNF

reinforced blended composite parent materials.

Figure ‎0.8 Comparison the modulus of elasticity

of the pure blended origami [35] with composite

origami cores.

Figure ‎0.9 Comparison the strength of pure

blended origami [35] with composite origami

cores.

Figure ‎0.10 Toughness of composite origami

cores.

4.3.2.2 Impact Test Results

The study in the previous section showed that the addition of the CNFs to the PLA/TPU blends

improves the elastic modulus, and the strength of the composite origami cores. In the case of

impact event, the higher strength altered the ability of the base material to work as a compliant

62

mechanism, and thus decreases the absorbed force and diminishes the energy absorption by the

cores, compared to pure PLA/TPU cores. Origami cores with high percentage of CNF tend to

fracture more than those of pure polymer blends. Most of the samples made of high PLA/CNF

composition break under the impact point (figure 4.11), and it is observed that the fracture

propagated through the crease lines, which is the weakest region in the origami structures. Some

PLA with high percentage of CNF samples, which are more rigid and brittle, were fractured even

through the rigid faces of the origami structures (figure 4.11C).

Figure ‎0.11 (a) Fractured PLA+1%CNF sample under the point of impact, (b) Propagation of

the fracture through crease line on a PLA+1%CNF sample, (c) fractured PLA+3%CNF sample.

Composite origami core samples with 80/20 PLA/TPU also experienced fracture through the

crease lines, when they were tested multiple times. This can be an indicator for the existence of

internal micro-fractures during the tests. Figure 4.12 shows a sample of force-time response

curve, which was used to calculate the transferred energy. The presented results in figure 4.13

show the higher maximum force transferred proportional with the higher amount of the CNF.

These values of the maximum force transferred are still lower than the values of force transferred

by steel, or polycarbonate plates tested in the same conditions, which proves the efficiency of

origami core structures in distributing the impact loads through its unique geometrical features.

The behavior of the composite origami cores seems to present two different zones, with the

65/35 PLA/TPU being in the middle. The samples above this composition showed brittle

behavior. Samples with neat PLA showed fractures and 80/20 PLA/TPU might have internal

63

fracture as explained above. This explains that these samples transferred forces to the bottom

side until they got facture, which decreased the transferred force they might transmit during the

impact event, and the slight difference in the force transmitted between neat PLA and 80/20

PLA/TPU, because of the small amount of TPU allowed the distribution of the impact force

before fracture.

The samples with PLA/TPU below 65/35 showed a flexible behavior allowed them to distribute

the incoming impact force through the origami structure, and as a result transferred less force to

the other sandwich side. The neat TPU samples showed a slightly higher transferred force than

the 20/80 PLA/TPU, because of the rubbery behavior of the TPU that allows the cores to densify

and transfer force. The 65/35 PLA/TPU composition benefits from the rigid behavior without

showing fracture and then transferred more force to the bottom side of the core. In Figure 14 the

maximum impact energy transferred by the composite origami cores is illustrated. It shows a

higher value with the increased amount of CNF, which might act against the brittle fracture of

the samples. Moreover, the samples that seem to transfer the least energy are 20PLA/80TPU, due

to their high flexible behavior, allowing compliant mechanisms on the creases, but preventing a

high deformation of the faces. Neat TPU with CNF seems to be the composition that transfers

the most energy, as explained before, due to the rubbery behavior, causing it to endure important

elastic deformation without any fracture and transfer force on a large scale of time compared to

the other compositions. The decreasing transferred energy for TPU with increasing amount of

CNF‎might‎be‎due‎to‎the‎improvement‎of‎the‎samples’‎rigidity.‎The‎results‎of‎the‎impact‎testing‎

showed that the addition of CNF increases the force transferred by the origami cores and

decreases the damping efficiency of the cores. Figures 4.13 and 4.14 illustrate the comparison of

impact force and impact energy transferred by origami cores made of composite origami and

pure blended origami [35]. Table 4.3 lists a comparison values of the maximum force transferred

by composite origami cores and the maximum force transferred by plane polycarbonate and steel

plats tested in the same condition [35].

64

Figure ‎0.12 Sample of impact force-time response.

Figure ‎0.13 Comparison of the max. force

transferred by pure blended origami cores [35]

with composite origami cores

Figure ‎0.14 Comparison of maximum impact

energy transferred by pure blended origami cores

[35] with composite origami cores.

Table ‎0.3 Comparison between the maximum force transferred by composite origami cores and

other plane materials.

CNF (w%) Material Blends Composition (PLA/TPU) w% Maximum force transferred (N)

1% 100/0, 80/20,65/35, (2574.26 – 3559.76)

65

50/50, 20/80, 0/100

3%

100/0, 80/20,65/35,

50/50, 20/80, 0/100

(3019.65 - 3829.513)

5%

100/0, 80/20,65/35,

50/50, 20/80, 0/100

(3184.39 - 4094.45)

Polycarbonate (11432.9) [35]

Steel (20852.0) [35]

4.3.3 Active Properties

4.3.3.1 Shape Memory Effect

The four steps of the shape memory test were performed on the composite origami unit cell, the

samples with high percentages of CNF showed no recovery during the shape memory test, the

1%, 3%, and the 5% CNF composite samples have showed no response during the recovery test.

This can be explained because of the existence of the carbon fibers which does not allow the

material to flow during the heating process, even when the material reaches the glass transition

temperature. The amount of fibers affects the flow of the polymer particles, and increasing the

stiffness of the composites which resist the activation force required to move the part.

In addition, the CNF affected the compression resistance when the samples heated during the

compression stage of the shape memory test, in which crack has been observed along the crease

lines on the origami unit cell (figure 4.15). The samples with small amount of CNF (0.1 wt %)

showed high response and high recovery ratio, due to the thermal response of the composite and

the less amount of the CNFs, the unite cell faces were able to move during the recovery test.

Figure 4.16 shows a compressed composite origami unit cell made of PLA + 0.1 wt % CNF after

shape fixing.

The compression-relaxation test results are shown in figure 4.17; the figure shows the maximum

stress reached by the origami unit cell was 0.348 MPa, and the tested sample relaxed in about

66

300 sec. The recovery test showed that the sample was able to recover its original height in about

63 sec. Figure 4.18 shows the height recovery versus time, and figure 4.19 shows the unit cell

height recovery during time. This results show that there is an enhancement in the recovery time

compared with the recovery time of the pure PLA samples tested in our previous work[40], in

which the pure PLA origami sample toke more than 450 sec to recover 85% from its original

height.

Figure ‎0.15 Cracked composite Origami unit

cell made of (PLA + 3wt % CNF)

Figure ‎0.16 Deformed composite origami unit

cell made of low percentage of CNF (PLA +

0.1wt % CNF)

Figure ‎0.17 Stress relaxation test of composite

origami sample made of PLA + 0.1wt% CNF

Figure ‎0.18 Recovery shape of composite

origami sample made of PLA + 0.1wt % CNF

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Figure ‎0.19 The origami unit cell recovery (height)

From the same material composition (PLA + 0.1 wt % CNF), origami samples were fabricated

and tested for compression and impact resistance. The results demonstrated that the elastic

modulus was 8.55 MPa, and the maximum force transferred by impact was 4195.95 N. These

results are comparable with the values obtained from the PLA+CNF samples.

4.4 Conclusion

The way the origami metamaterial can redistribute compression and impact forces make it

qualified for potential use in future applications, as a light-weight sandwich core. The use of

CNF with the material blends to fabricate composite origami structures significantly enhances

the overall mechanical properties of the origami cores in compression, in which the compressive

modulus and the strength of the origami cores were increased by the increase of the CNF. By

noting that samples with high PLA content face fracture through the crease lines, while low PLA

samples showed more elastic behavior. The impact testing showed a higher transferred force and

energy for higher carbon nanofiber compositions, because of the increasing in the rigidity of the

samples. 65PLA/35TPU showed the highest transferred force because of the coupling effect of

rigidity, flexibility and fiber reinforcement, while the higher PLA composition samples showed

major brittle behavior and the lower PLA composition samples showed flexible behavior. The

DSC test results showed an improvement in glass transition for both TPU and PLA with the

increasing amount of CNF, and the DMA results showed a significant increasing of the storage

modulus and a slight improvement of the loss modulus. Active composite origami structures

showed fractures along crease lines and low recovery ratio, composite origami with low CNF

percentages (0.1%) showed good stress relaxation behavior and high recovery ratio.

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[28] Song J J, Chang H H and Naguib H E 2014 Design and characterization of porous

biocompatible shape memory polymer (SMP) blends with a dynamic porous structure

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[29] Small W, Singhal P, Wilson T S and Maitland D J 2010 Biomedical applications of

thermally activated shape memory polymers. J. Mater. Chem. 20 3356–66

[30] Tobushi H, Hara H, Yamada E and Hayashi S 1996 Thermomechanical properties in a thin

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Chapter 5.

3D Printing of Ron-Resch-Like Origami Cores for Compression and Impact Load Damping3

Core panels made of origami structures provide effective force redistribution and energy

dissipation. A wide range of origami patterns is proposed to create three-dimensional panels,

which can be used as sandwich cores. The origami tessellation mainly consists of unit cells made

of small faces joined together through crease lines. Ron-Resch is an origami pattern composed of

star pleats joined together that exhibits pronounced shape flexibility and geometry forming as

well as potential mechanical performance. These advantages can be employed for load

dissipation and damping due to its high deformation and strain values. This study focuses on

three different Ron-Resch-like‎origami‎tessellations‎based‎on‎the‎star‎pleat’s‎number‎of‎branches‎

and the area of internal facets of the star pleat. An additive manufacturing technique was used to

fabricate the tested samples from polylactic acid (PLA) filament. In addition, compression and

impact tests were conducted to evaluate the effect of the folding angle for three different angles

and then the results have been discussed. The ANSYS finite element package was used to

numerically simulate the compression and impact events Moreover; the study includes

investigation of the shape memory effect based on the shape recovery of the unit element of the

Ron-Resch-like origami tessellation.

3 The content of this chapter has been published in the Journal of Smart Material and Structures;

Kshad, M.A.E., Popinigis, C., and Naguib, H.E., 2018. 3D printing of Ron-Resch-like origami cores for

compression and impact load damping. Smart Materials and Structures, 28(1), p.015027.

https://doi.org/10.1088/1361-665X/aaec40

73

5.1 Introduction

The idea of folding based on origami, in which a flat sheet of material is converted to a three-

dimensional structure, has recently attracted attention for a wide range of applications. The shape

and the geometry of the generated three-dimensional (3D) structures depend on the designed

pattern of the origami tessellation. There are limitless ways of creating origami patterns to

produce different 3D structures; Miura and Ron-Resch are types of origami patterns that have

attracted the attention of engineers to study their behaviors and geometrical characteristics. As an

example, Miura origami has been used and employed in many applications such as core

structures and solar panels [1–9]. The capacity of origami cores to redistribute forces and

dissipate energy is based on the degree of the reentrant of the origami unit cell elements during

the folding and unfolding process, which results in high deformation of the origami structure

elements. In the 1970s, Resch [1,10] suggested Ron-Resch origami, which has the ability to form

curved panels when partially folded. Tomohiro et al. [11] suggested a new method to avoid the

intersection between facets sharing vertices in which a star-like folded tuck is inserted to

generate the tessellation of a Resch origami structure [11]. Origami structures as periodic cellular

structures have demonstrated promising performance for compressive and impact loads

resistance which can be employed in lightweight structures [12–14]. Rapid advances in

manufacturing technology, especially additive manufacturing, provide a great opportunity for

fabricating and investigating complex origami and foldable structures [2]. Another study by Bok

Yeop et al. [15] focused on the possibility of printing origami structures by designing a highly

concentrated ink to produce printed structures for wet-folding origami. Theoretical,

mathematical, and numerical analyses of different origami patterns have been extensively

covered in previous research studies [16–25]. Elastic metamaterials also can be used in impact

attenuation, KT.Tan at el. [26] proposed a single-resonator model and dual resonator

microstructural design, and simulated the effect of negative effective mass density. Another

study done by Zhao at el. [27] investigated the effect of the pore size on the stress wave

propagation across silica nano-foams.

In this study, we investigate different Ron-Resch-like origami configurations by changing the

number of star tuck branches and the angle between the internal faces of the star tuck. Three-,

four-, and six-branch star pleats were studied with three different folding angles (15, 30, and 60

degrees). The selected geometries were designed to form flat panels. The designed models of the

74

Ron-Resch-like origami tessellation were fabricated using 3D printing. The material used for

fabricating the origami cores was Polylactide (PLA). The fabricated samples were tested for

compression and impact to predict the compressive properties of the tested panels; we also

investigated damping upon load application. The compression results revealed that the tested

panels can withstand high compression stress before plastic deformation. Furthermore, the tested

panels exhibited a high degree of impact resistance and energy dissipation compared with other

origami panels tested in the same conditions. The ANSYS finite element package was used to

simulate the compression test for the nine models. Moreover, an explicit dynamics analyzer was

used for the impact event simulation. Furthermore, the designed samples were also tested for

shape recovery by applying the steps of the shape memory effect and measuring the shape

recovery of the unit element of the Ron-Resch-like elements.

5.2 Experimental work

The 3D structure of Ron-Resch‎origami‎ is‎characterized‎ by‎ the‎dimensions‎of‎each‎unit‎ cell’s‎

polyhedron and the angle between the elements of the unit cell tessellation. Figures 5.1 and 5.2

show the geometrical parameters of the Ron-Resch-Like origami unit elements and panels. The

overall dimensions of the panel were 120 x 120 x 10 mm, and the thickness of the origami

elements was 11.3 mm (Figure 5.3). Table 5.1 lists the dimensions of the designed Ron-Resch-

Like origami patterns.

Figure ‎0.1 The designed Ron-Resch-like origami unit elements, a) RR – 3, b) RR – 4, and

c) RR – 6.

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Figure ‎0.2 The designed tessellations of Ron-Resch-like origami panels, a) RR – 3 – 15,

b) RR – 3 – 30, c) RR – 3 – 60, d) RR – 6 – 15, e) RR – 6 – 30, f) RR – 6 – 60, g) RR – 4 – 15,

h) RR – 4 – 30, i) RR – 4 – 60.

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Figure ‎0.3 RR-3-30 model, (a) a 3D view of Ron-Resch-like origami panel (b) the in-plane

dimensions in mm of origami panel, and (c) the basic element configuration of the origami.

Table ‎0.1 The dimensions of the designed Ron-Resch-like origami unit cells.

Sample Fold Angle H (mm) L (mm) W(mm)

RR – 3 -15 15 11.3 28.442 10.501

RR – 3 -30 30 11.3 29.571 12.326

RR – 3 -60 60 11.3 30.516 17.46

RR – 6 -15 15 11.3 31.86 11.76

RR – 6 -30 30 11.3 36.844 16.28

RR – 6 -60 60 11.3 44.396 26.852

RR – 4 -15 15 11.3 20.93 10.26

RR – 4 -15 30 11.3 22.41 11.5

RR – 4 -15 60 11.3 24.52 15.21

5.3 Fused Deposition Modeling (FDM) for Fabricating Origami Structures

Fused deposition modeling (FDM), also known as 3D printing, was used to fabricate the

designed origami panels. A MakerBot 3D printer was used with PLA with a diameter of 1.75

77

mm, which was provided by Spool Works. The fabrication conditions were as follows: the

extruder temperature was set at 240°C, the layer height was 0.20 mm, the infill was 25%, and the

number of shells was two. The mechanical properties of the PLA filament were measured using

the Instron tensile machine Micro-tester (Model 5848), and the tensile test was conducted in

accordance with the ASTM D638. Figure 5.4a shows the 3D-printed Ron-Resch-like origami

panel, and Figure 5.4b shows the fabricated Ron-Resch-like unit element. The nine models of the

fabricated Ron-Resch-like origami panel are illustrated in Figure 5.5. Also, the single unit

elements of the fabricated Ron-Resch-Like origami of the nine models are shown in Figure 5.6.

Figure ‎0.4 (a) Fabricated Ron-Resch-like origami panel (b) Ron-Resch-like element.

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Figure ‎0.5 3D-printed Ron-Resch-like origami panel, a) RR – 3 – 15, b) RR – 3 – 30,

c) RR – 3 – 60, d) RR – 6 – 15, e) RR – 6 – 30, f) RR – 6 – 60, g) RR – 4 – 15, h) RR – 4 – 30,

i) RR – 4 – 60.

79

Figure ‎0.6 3D-printed Ron-Resch-Like origami unit cell, a) RR – 3 – 15, b) RR – 3 – 30,

c) RR – 3 – 60, d) RR – 6 – 15, e) RR – 6 – 30, f) RR – 6 – 60, g) RR – 4 – 15, h) RR – 4 – 30,

i) RR – 4 – 60.

5.4 Mechanical Testing Procedure

5.4.1 Compression Test

Compression tests were conducted to estimate the capacity of the fabricated origami cores to

withstand compressive loads. The general tensile/compression testing machine was used to run

the compression test: the sample was placed between two thick plates connected with the testing

machine to enable uniform distribution of the compression loads. The test was conducted in

accordance with ASTM D1621/94 standards. The force-displacement relation was measured.

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5.4.2 Impact Test

To conduct the impact test, each sample was sandwiched between two polycarbonate sheets by

placing epoxy glue in the tips or on the upper and lower surfaces of the core. Then, the sandwich

structures were placed on top of the testing plate of the impact setup. The testing plate was

connected to a load sensor (Dytran1060v) to measure the transferred load. The sensor was then

connected to the data acquisition system to record force versus time. The test was conducted in

accordance with ASTM D7766/D7766M standards. The drop distance was 66.5 cm, and the

testing drop weight was 1.104 kg.

5.5 Modeling of Ron-Resch-Like Origami Panels

5.5.1 Compression Test Simulation

To perform the compression test simulation, we used the ANSYS static structural solver. The

Ron-Resch-like origami core was placed on a thick rigid steel plate, and the load was applied as

a strain displacement of 7 mm. The cores were represented by shell elements, and the lower thick

plate was represented by a rigid body with a fixed boundary condition in the lower face of the

plate. Figure 5.7 shows the modeled Ron-Resch-like origami panel for compression.

5.5.2 Impact Test Simulation

The simulation of impact test was performed using the ANSYS explicit dynamics solver. In this

simulation, the sandwiched Ron-Resch-like origami core was represented by shell elements, and

the mesh was fined for accuracy using the solution conversion to select the proper size and

number of elements and nodes taking into account the thickness of the core panel. The impactor

was considered as a rigid body with a mass of 1.104 kg. The impact speed was 3.63 m.s-1

, and

standard earth gravity was taken to be 9.81 m/s2. Figure 5.8 shows the modeled Ron-Resch-Like

panel for impact.

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Figure ‎0.7 Compression model of the Ron-

Resch-like core panel (RR – 3 – 15).

Figure ‎0.8 Impact model of the Ron-Resch-Like

core panel (RR – 3 – 15).

5.6 Shape Recovery of Ron-Resch-Like Origami Unit Element

The shape memory effect test was conducted on the Ron-Resch-Like unit elements (Figure 5.6).

The basic steps of the test included the compression test, the relaxation test, shape fixity, and

shape recovery. The compression-relaxation test was carried out using Instron Micro-tester

(Model 5848), and the test was conducted with a loading rate of 1.3 mm/min as per ASTM

(D695); the conditional temperature was 75C, which was just above the glass transition

temperature of the base material. We performed the fixing process to fix the deformed samples

by soaking the sample in a cold water bath. To recover the original geometry of the samples, we

used an isolated thermal chamber in which the temperature was kept to 75C; we then measured

the height change as a function of time.


5.7.1 Compression test results

The compression test results of Ron-Resch-like origami cores show that the compression

behavior of the tested samples was consistent, Figure 5.9 shows the compressive stress-strain

relation of the tested cores. and the values of the compression modulus were as follow: for the

RR-3-60 was 2.97± 0.07 MPa, RR-3-30 was 3.95 ± 0.19 MPa, RR-3-15 was 11.04 ±1.56 MPa,

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RR-4-60 was 2.85±0.041 MPa, RR-4-30 was 7.20±1.61 MPa, RR-4-15 was 11.82 ±2.5 MPa,

RR-6-60 was 0.42±0.08 MPa, RR-6-30 was 1.19±0.07 MPa, and RR-6-15 was 4.84 ±0.08 MPa,

Figure 5.9d. The results revealed that the specific compressive modulus of elasticity decreases

with increasing folding angle; we also observed that the number of star-tuck branches

significantly affected the compressive modulus. Figure 5.10 illustrates the comparison of the

specific compressive modulus of elasticity with respect to the number of star-tuck branches and

the folding angle. The star-tuck panel with four branches (RR – 4) exhibited the highest modulus

of the three examined folding angles (i.e., compared with the three (RR – 3) and the six (RR – 6)

star-tuck branches. The three RR-3 models showed higher values of the compressive moduli

compared with the three models of the RR-6, because the RR-3 samples have more unit cell units

in the panel, and the RR-6 models have less, which refers to as (the intensity of the unit cells).

The samples exhibited a plastic deformation at the tips of the star tuck (Figure 5.11). We

observed that the deformation propagated to the mid-plane of the origami core; while the upper

part of the star tuck above the mid-plane did not exhibit any plastic deformation because of the

high stress concentration in the star tuck edges and tips (Figure 5.11).

Figure ‎0.9 Compressive stress-strain relations of a) RR – 3, b) RR – 4, c) RR – 6, d) Comparison

of the compressive modulus.

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Figure 5.10 Specific modulus of elasticity of a) RR – 3, b) RR – 4, c) RR – 6.

Figure ‎0.10 Plastic deformation on the tip of the star tuck of the Ron-Resch-like origami

element.

5.7.1.1 Collapse Mechanism of Ron-Resch-like origami cores

Collapse mechanism in the Ron-Resch-Like Origami cores under compression or impact loading

is due to elastic buckling of the internal plate-like faces followed by plastic hinges across planes

in perpendicular directions to the loading path. Compression curves of Ron-Resch-Like Origami

cores in figure 5.9 suggest similar behavior to porous structures under compression. The

compression process starts linear at the first phase of loading until reaching the point of

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instability (or collapse) at which the structure continues to deform in compression but with

relatively constant stress for large strain values up to the point of complete collapse of all internal

walls where the process of densification initiates with sharp increase in the compression stress at

relatively constant strain. Collapse can be better studied by studying the buckling of internal

faces and avoid the formation of plastic hinges. That is because once plastic hinges formed then

heating is required to bring the structure back to its virgin state. However, the study of buckling

should provide guidelines to alleviate the collapse of Ron-Resch-Like Origami cores similar to

porous structures. The complexity of buckling analysis arises from the common edges between

internal faces which may suggest coupled or concurrent buckling for several faces at the same

time. Nevertheless, the study of an isolated face under different folding angles will certainly

provide an insight to the overall collapse behavior of the proposed Origami structures. Buckling

can be defined as the condition in which loads are large enough to destroy the stability of an

equilibrium configuration [28]. Buckling may occur by bifurcation, which means that a reference

configuration of the structure and an infinitesimally close (buckled) configuration are both

possible at the same load. Buckling may also be associated with a limit point where stability is

lost but there is no immediately adjacent equilibrium state.

The following discussion is proposed to analyze the buckling of internal faces but limited to

linear bifurcation buckling. The first step is to load the structure by an arbitrary reference load

Rref, and perform a linear viscoelastic analysis to determine the in-plane stresses. A stress

stiffness matrix for the reference load can be defined as:

(1)

where;

(2)

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G is‎a‎matrix‎contains‎shape‎functions’‎derivatives.‎More‎details‎can‎be‎referred‎to‎[28].

For some other load level, with multiplier,

when (3)

Let buckling displacement takes place relative to displacement of the reference

configuration. Because the external loads do not change at bifurcation point,

(4)

This last equation (4) is an eigenvalue problem whose smallest root defines the smallest level

of external load for which there is bifurcation, namely,

(5)

Up to this point, the force calculated from equation (5) represents the critical buckling load

required to initiate the collapse of the internal faces followed by the formation of plastic hinges.

The difficulty in analyzing polymeric plate-like structures of the internal faces arises from the

viscoelastic nature of this class of material. The constitutive law for PLA can be assumed as a

linear viscoelastic model based in Boltzmann superposition principle. For viscoelastic materials

in general, the relationship between stress and strain depends on time, and they have three

important properties: stress relaxation, in which with a constant strain the stress decreases, creep,

in which with a constant stress the strain increases, and hysteresis which is a stress-strain phase

lag. All features are preserved in the linearity assumption except that the time dependency of

material properties is simplified to ignore aging effects with a fading memory assumption.

86

Moreover, linear viscoelasticity is valid for small strains only. In experimental tests on

viscoelastic materials, it is observed that the instantaneous changes in stress or strain are

governed, at the instant, by‎Hooke’s‎law,‎that‎ is,‎ the‎instantaneous‎response‎is‎elastic‎[29].‎The‎

effect of strain history can be approximated by piecewise constant step functions and superposed

to the elastic response. This yield the following constitutive law [30]:

(6)

where is the history variable and D is the stress relaxation matrix obtained experimentally.

Equation (6) can be solved numerically with finite element method in a procedure with equations

(1-5) to predict the buckling load of internal plate-like faces of the Ron-Resch-Like Origami

structures. More details can be found in a similar work presented in reference [31], also the

buckling behavior of RR-3-30 model with comparison with Miura model has been presented by

the authors in [32].

5.7.2 Impact Test Results

The impact test results yielded a force-time response; this force represents the transferred force

through the sandwich structure. Figure 5.12 shows the force-time response received by the force

sensor; figure 5.13 compares the maximum force transferred by the Ron-Resch-like cores. The

results reveal that RR – 6 transferred the least amount of impact force compared with RR-3 and

RR-4 for folding angles of 30 and 60. In the case of the 15 folding angle, RR – 3 transferred

the smallest impact force, and the RR-4 models transferred the largest amount of the impact

force. The maximum transferred force was 3.9 KN by RR – 4 – 15, and the minimum force

transferred was 2.3 KN by RR – 6 – 60. The transferred force decreased with increasing folding

angle (Figure 5.13). Table 5.2 lists the values of the maximum force transferred by the Ron-

Resch-like sandwich cores and previously tested origami cores made of PLA and polycarbonate

sheet and steel plate tested in the same conditions [33]. It is clear that the Ron-Resch-like

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sandwich cores transferred less impact force. However, this situation persisted at the expense of

a plastic fracture in the central tip of the star tuck.

Figure ‎0.11 Transferred impact force.

Figure ‎0.12 The maximum impact forces

transferred by the Ron-Resch-like panels.

Table ‎0.2 Comparison of maximum impact force transferred.

Material Maximum Force Transferred (N)

RR-3-15 ~2900

RR-3-30 ~2750

RR-3-60 ~2500

RR-4-15 ~3900

RR-4-30 ~3600

RR-4-60 ~3000

RR-6-15 ~3400

RR-6-30 ~2600

RR-6-60 ~ 2400

PLA - Miura Origami core [33] 3708.2

Polycarbonate [33] 11432.9

Steel [33] 20852.0

5.7.3 FEM Simulation Results

A compression simulation of the Ron-Resch-like cores was conducted using the ANSYS

structural static solver. The results revealed that the cores exhibited high strain deformation

during compression. The stress distribution on the cores showed that the maximum stress

concentration‎occurred‎in‎the‎tips‎of‎ the‎star‎ tucks‎and‎didn’t‎persist‎further‎ through‎the‎crease‎

88

lines; it did not exceed far through the star tuck high, which was consistent with the experimental

results (Figure 5.14).

Figure 5.15a illustrates the total deformation of the RR – 3 – 15 model, in which the maximum

value of the total deformation was roughly 8.0 mm. Figure 5.15b shows the directional

deformation of the RR – 3 – 30 model in which the maximum directional deformation in the y

direction was roughly 7 mm. Figure 5.16 compares the maximum total deformation and the

maximum equivalent stress of the nine core models. It is clear that the folding angle affected the

deflection and the stress on the simulated cores (Figure 5.16). The FEM simulations revealed

consistency in the impact behavior of the origami cores and their directional deformational. This

finding explains the ability of the structure to redistribute applied force and absorb energy.

Figure 5.17 illustrates the results of finite element simulations for RR – 3 – 15. The results of the

impact simulation are shown in Figure 5.18, which illustrates the effect of the folding angle and

the number of star-tuck branches on the transferred impact force. This figure shows that the

maximum transferred force decreases with increasing folding angle.

Figure ‎0.13 The compressive deformation of the RR – 3 – 15 model compared with the tested

sample.

89

Figure ‎0.14 a) The total compressive deformation of the RR – 3 – 15 model, b) the directional

compressive deformation (y-direction) of the RR-3-30 model.

Figure ‎0.15 Comparison of a) maximum total deformation, b) maximum equivalent stress.

Figure ‎0.16 . a) The total deformation due to impact event (RR – 3 – 15), b) the equivalent von-

Mises Stress distribution on the model (RR – 6 – 15).

90

Figure ‎0.17 Comparison of the maximum transferred force by impact.

Figure 5.19 comparing the deflection behavior of the simulated samples, as we can see the tips of

the Ron-Resch-like unit cell is the most deformed part of the structure, the value of this

deflection is depending on the star-tuck angle and the number of star-tuck branches. Elements

with small angles exhibited high deformation closed to the tips with less deformation distribution

along the star branches. From the other hand, the Ron-Resch-like models with higher angles

exhibited less deformation on the tops but with more spread of the deformation, as we can see in

figure 5.19. Furthermore, by the increasing of the star-tuck branches the maximum deformation

increases as shown in figure 5.20. Figure 5.21 showing the deformed star-tuck braches of the

tested models.

a) RR-3-15

b) RR-3-30

c) RR-3-60

d) RR-4-15

e) RR-4-30

f) RR-4-60

91

g) RR-6-15

h) RR-6-30

i) RR-6-60

Figure ‎0.18 The deformation of the star-tuck-edges.

a) RR-3-15

b) RR-3-30

c) RR-3-60

d) RR-4-15

e) RR-4-30

f) RR-4-60

g) RR-6-15

h) RR-6-30

i) RR-6-60

Figure ‎0.19 The deformation of the star – tuck branches of Ron-Resch-like origami panels.

92

Figure ‎0.20 The FEM results of the maximum deformation of the Ron-Resch tested models

5.7.4 Shape Recovery Results

The shape memory test steps were performed on the Ron-Resch-like unit elements. Figure 5.22

shows the three phases of the geometry changing during the shape memory effect test: the

original shape, the deformed and fixed shape, and the recovered shape. The results of the shape

memory effect of the Ron-Resch-Like origami unit elements are summarized in Figures 5.23 and

24. The results of the stress relaxation test are illustrated in Figure 5.23, in which one can see the

effect of the folding angle on the maximum stress values of the unit elements. The curves show

that the tested samples started to relax after 200 sec. The height recovery measured versus time

relations are shown in Figure 5.24. One can see that the RR – 3 models recovered most of their

original height in less than 60 sec; the RR-4 and RR – 6 models only partially recovered their

original height. The RR – 6 model recovered up to 80% of its original height for folding angles

of 15 and 30 and less than 70% of its original height for a folding angle of 60. The RR– 4

model recovered more than 60% of its original height for a folding angle of 30 and less than

50% of its original height for folding angles of 15 and 60.

Un-deformed

Deformed

Recovered

Figure ‎0.21 The three phases of the geometry changes during the shape memory effect test.

93

Figure ‎0.22 Compression and stress relaxation results of the Ron-Resch-like origami unit

element, a) compression of RR – 3, b) stress relaxation of RR-3, c) compression of RR – 4,

d) stress relaxation of RR – 4, e) compression of RR – 6, and f) stress relaxation of RR - 6

(a) (b)

(c) (d)

(e) (f)

94

Figure ‎0.23 Shape recovery of the Ron-Resch-like origami unit element, a) RR-3, b) RR-4, c)

RR-6, d) comparison of the height recovery ratio.

5.8 Conclusion and Future Directions

Advances in designing and investigating origami-inspired materials can lead to the production of

materials with properties that can be used in a wide range of applications that require high loads

and energy damping. In this work, Ron-Resch-Like flat origami panels were fabricated by 3D

printing, and the material used was PLA filaments. The fabricated samples were tested in

compression and impact. The impact results revealed that the Ron-Resch-Like cores have

advance for damping impact forces and dissipating energy compared with Miura origami cores.

However, the Ron-Resch-like cores exhibited a single fracture in the tip of the star tuck. Fused

deposition modeling can be used to fabricate such complex origami configurations. Different

Ron-Resch configurations should be characterized and compared to optimize the best

geometrical parameters. Optimization and finite element simulation should be conducted to

(c) (d)

(a) (b)

95

compare the parameters of the designed cores. It is important to design ink material for 3D

printing that can be used with 3D printers for different applications.

96

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Origami Structures, (2010) 2251–2254. doi:10.1002/adma.200904232.

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analysis of deployable origami tessellation, Comput. Aided. Des. Appl. 10 (2013) 939–

951. doi:10.3722/cadaps.2013.939-951.

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[18] M. Schenk, S.D. Guest, Origami Folding: A Structural Engineering Approach, Origami 5

Fifth Int. Meet. Origami Sci. Math. Educ. (2011) 1–16.

[19] J.L. Silverberg, A.A. Evans, L. McLeod, R.C. Hayward, T. Hull, C.D. Santangelo, I.

Cohen, Applied origami. Using origami design principles to fold reprogrammable

mechanical metamaterials., Science. 345 (2014) 647–50. doi:10.1126/science.1252876.

[20] N. Turner, B. Goodwine, M. Sen, A review of origami applications in mechanical

engineering, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 0 (2015)

0954406215597713–. doi:10.1177/0954406215597713.

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Spat. Struct. 50 (2009) 2287–2294. http://dspace.upv.es/manakin/handle/10251/6828.

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[23] S.‎ Waitukaitis,‎ R.‎ Menaut,‎ B.G.‎ Chen,‎ M.‎ Van‎ Hecke,‎ Origami‎ Multistability :‎ From‎

Single Vertices to Metasheets, 055503 (2015) 2–6. doi:10.1103/PhysRevLett.114.055503.

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compressive loads facets under compressive loads, SPIE, March 2018, 1059600, (2018)

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99

Chapter 6.

Modeling and Characterization of Viscoelastic Origami Structures Using Temperature Variation-based Model4

Recently, the use of origami cores in sandwich structures attracted increasing attention in many

engineering applications due to its compromising between the weight and strength, and its ability

to dissipate incoming loads. The modeling of origami cores is one of the strongest tools that used

to estimate the design parameters for high performance. The main outcome of this work is to

provide a general platform of modeling polymeric origami cores by considering the viscoelastic

properties of the base material at elevated temperatures and applying periodic boundary

conditions. The model considered a single origami unit cell as a representative unit element,

which is consists of the repeated elements of the origami structure. Periodic boundary conditions

were applied in the shared edges of the repeated unit cells. Furthermore, the work shows the

results of multi-unit cell origami panel using the viscoelastic model.

4 The content of this chapter submitted to the Journal of Intelligent Materials and Structures.

100

6.1 Introduction

The use of sandwich structures is very common in many applications that require low density

and high load resistance. Such structures are mainly made of well-designed core sandwiched

between two faces. There are many types of sandwich cores used in sandwich structures, such as

honeycomb, corrugated panels, foamed, and folded and origami cores. The use of origami cores

in sandwich panels has gained more interest during the last years [1]. Origami is a naturally

inspired idea, it started as an art of paper folding for decoration [2], then the idea got attention for

sandwich cores due to high deformation and load dissipation. The design of sandwich cores must

consider the weight and the targeted mechanical properties. The geometrical and mathematical

features of different designs of origami tessellations have been addressed in much previous

research [3–5].

The work introduced by Eidini. et al. [6], provided analytical and numerical models of folded

material that can exhibit both negative and positive in-plane‎Poisson’s‎ratios.‎Schenk‎and‎Guest‎

[7], described the geometrical details of two metamaterials based on Miura origami structures

that key paly role in its mechanical properties. The morphing origami structures has got big

interest in previously done research [8,9]. Gattas et al. [8] introduced alternative mechanism for

rigid Muira origami morphing sandwich. V. Aminzadeh et al. [10], investigated various

geometrical types of origami cartons to develop analytical models for the folding characteristics.

Wonoto et al. used Non-linear finite element analysis with parametric system, geometric

scripting utilized to study the geometrical features of Miura-origami structures [11]. The

modeling of origami cores can give a deep understanding of the deformation behavior of the

origami unit cell element. Several studies have been done in modeling sandwich and origami

structures, using different approaches [12–14]. A. Lebée et al. used the unit load method to

derive the effective transverse shear moduli of folded sandwich cores type chevron [15], they

also provided a finite element study of folded structure core applying bending-gradient

homogenization scheme, the study showed that the skin distortion influences the shear stiffness

of the sandwich [16], Another research presented by the same authors, introduced the application

of Bending-Gradient plate theory to cellular sandwich panels [17]. Baranger et al. introduced a

numerical modeling procedure of geometric defects based on the folding process [18]. Another

research was done by Pereza et al. use a computer-aided design technique to model origami

structures with smooth folds [19]. Regular origami structures mainly consist of periodic unit

101

cells, each unit cell composed of small elements representing the faces of the unit cell. A

periodic boundary condition can be implemented to simulate the periodicity of the unit cell [20].

In the present work, a representative unit cell was used to simulate polymeric origami structure;

the work adopted the use of periodic boundary condition to simulate the representative unit cell

[16,20]. The novelty of this work is to provide a general skeleton to predict the mechanical

properties of origami structure using a representative unit cell and by including the viscoelastic

properties of the base material. The model considered the viscoelastic behavior of the material at

elevated temperatures. For viscoelastic analysis the relaxation modulus measured at different

temperatures. The relaxation moduli were measured at four different temperatures below the

glass transition of the base material. The temperature levels were: 25 C, 35 C, 45 C, and 55

C. The studied origami pattern was Miura origami, which is consists of periodic unit cells

connected throughout the pattern lines. The single unit cell is composed of four similar faces

joined together through crease lines. The results of viscoelastic model showed that the behavior

of the origami model was very similar to the experimental results in low temperature, and it has

some deviation in the high temperature case.

6.2 Experimental Procedure

Relaxation test has been carried out on dog-bone specimens made by fused deposition modeling,

the fabrication conditions were: extruder temperature 230 C, infill density 30%, infill layer

height 0.1mm, and the PLA filament diameter 1.77 mm. The test was conducted using Instron-

5848-microtester tensile machine in compression mode. The test procedure was according to

ASTM D638 -14 and ASTM 2990-01. The specimen kept under constant stain allowing it to

relax. The stress relaxation curves were obtained from the test, and then the relaxation modulus

was calculated. Furthermore, origami unit cells have been fabricated using fused deposition

modeling with the same settings that used to produce the dog-bone samples. Compression test

was performed on the fabricated origami samples using Instron-5848-microtester tensile

machine, in compression mode, with a strain rate of 1.3 mm/min.

102

6.3 Finite Element Modeling

The description of the finite element modeling of origami unit cell structure is described in this

section, to predict the mechanical properties of the origami structure such as modulus of

elasticity‎and‎Poisson’s‎ratio.‎The‎primary‎mechanical‎response‎is‎obtained‎according‎to‎ASTM‎

D 2990 and the Test Method D 638 using Instron Micro-tester (Model 5848). This is an input to

the unit cell of Origami structure with the application of periodic boundary conditions. The

procedure represents a homogenization step prior to analyzing origami structures with multiple

unit cells as a plate-like structure.

6.3.1 Finite Element Geometry and Boundary Conditions

Displacement-based periodic boundary conditions were assumed to the edges of the

representative unit cell (RUC) shown in figure 6.1. The periodic boundary conditions are carried

out in the opposite edges of the (RUC) in which the relative displacement between these edges

maintained to be zero. The distance between these opposite edges is one of the characteristics of

the unit cell, which is representing the length of the unit cell (L). The displacement function

vector ; can be expressed as following:

(1)

where and are the three Cartesian coordinates.

103

Figure ‎0.1 The representative unit cell (RUC) of the origami structure.

Linear constraint equation in ABAQUS was used to implement the periodic boundary condition

of the (RUC). The constraint equation is presented as [21], [16];

(2)

where R is node index, k is degree of freedom, i.e. 1, 2, and 3 which represent and

directions respectively, is a constant coefficient that defines the relative motion of nodes, is

the deformation of an arbitrary dummy node which is set to the target strain value.

The edges of the unit cell are inclined in 2D planes for all the sides which make it difficult to

apply the periodicity condition directly to the nodes since the motion of the nodes is always

characterized in two dimensions at least. This difficulty was alleviated by generating multi-point

constraint (MPC) in ABAQUS to the edges where periodicity to be applied. Thus the periodicity

condition is applied to the control points (MPC point) as shown in figure 6.2. ABAQUS uses

connectors (like beam elements in this study) to define multi-point constraints between a point

and slave nodes in a region. So the relative zero displacement is defined between MPC points 1

and 2 respectively. This periodicity condition will be applied to all the respected nodes along the

two edges being constrained.

104

Figure ‎0.2 Application of periodic boundary conditions in ABAQUS.

The opposite edges of the (RUC) should have traction continuity by having equal displacement

magnitude but in opposite sign. However, it was shown in [22] that analyzing the (RUC) with

displacement method in finite element, can guaranteed the uniqueness of the solution only by

equation (1) and thus traction continuity is automatically satisfied.

6.3.2 Viscoelastic Materials in ABAQUS

ABAQUS offers a time domain viscoelastic model for small strain applications, in which a linear

elastic material model can represent the rate-independent elastic response, which is similar to the

case of this work. In relaxation test, a strain is applied to the test specimen and then held

constant for a long time. The loading history is accounted from the zero time, and the zero time

is considered from the moment of applying the constant strain. The viscoelastic material model

in ABAQUS defines the varying stress with time, , [23] as:

(3)

105

where is the time-dependent relaxation‎modulus‎that‎characterizes‎the‎material’s‎response.‎

The used model is a long-term elastic (viscoelastic) in which the material is subjected for a long

time to a constant strain, and as a result the stress goes down to a constant value;

i.e., as where is long-term modulus. The relaxation modulus can be

written in dimensionless form [23]; , where is the instantaneous

relaxation modulus. So the expression for stress in ABAQUS takes the form;

(4)

The values of the dimensionless relaxation function are limited between and

.

In the ABAQUS FE solver either stress relaxation or creep data can be used as time-dependent

viscoelastic properties. The creep compliance (J) data can be converted to stress relaxation by

using the equation:

(5)

In general, but in the limits of then . For the FE analysis solver,

compliance data are normalized with respect to the instantaneous modulus of the material [24].

Hence, it is not necessary to specify precisely the creep compliance for ABAQUS input data. In

practice, normalization can be calculated with respect to the initial elastic displacement. After

106

applying the force, and measuring , were measured. The normalized creep compliance,

, is calculated as [24]:

(6)

The times (t) are considered after the application of the load. will be 1 at time = 0 and will

increase with time.

ABAQUS requires the experimental relaxation test data to be fitted to Prony series in the form;

(7)

where and are material constants.

One term Prony series is assumed for this study, and hence equation (7) reduces to;

(8)


Figure 6.3 shows the stress relaxation curves along with the one-term fitted Prony series. Table

6.1 lists the fitting parameters according to equation (8). The parameters in table 6.1 are the

input to ABAQUS as the material property constants.

107

Figure ‎0.3 . Experimental results of the relaxation modulus to one-term Prony series, a) T=25

C, b) T=35 C, c) T=45 C, d) T=55 C.

Table ‎0.1 Fitting parameters of one-term Prony series according to equation (8).

T = 25 °C 0.371 0.192

T = 35 °C 0.383 0.265

T = 45 °C 0.495 0.297

T = 55 °C 0.60 0.30

6.4.1 Compression Test Results of Origami Unit Cell

The results of the compression test of the origami unit are shown in figure 6.4. The figure shows

the compression behavior of the unit cell under elevated temperatures. The results show that by

b)

c) d)

a)

108

the increase of the temperature the material stiffens decreases. The maximum stress decreased by

20% when the temperature increased from 25 C to 35 C, and it was decreased by 60%

when the temperature was decreased from 35 C to 45 C. while it decreased up to 60%

between 45 C to 55 C.

Figure ‎0.4 Compression behavior of the origami unit cell at different temperatures

6.4.2 Correlation Analysis and Regression

The summary of key experimental/fitting results is presented in table 6.2. These parameters

include the relaxation modulus/time with respect to temperature in addition to the elasticity

modulus of the whole Origami structure. Linear correlation coefficients are calculated between

those parameters. The correlation coefficient can determine the strength and nature of the

relationship among the different parameters. These coefficients are useful and deterministic to

draw inferences about the strength of association between the parameters. The equation for the

correlation coefficient is [25]:

(9)

109

where x and y represent the two values required for to calculate the correlation coefficient, and

and are the averages of x and y respectively.

Table ‎0.2 Summary of experimental/fitting results.

T C Relaxation Time Sec

(MPa)

(MPa)

25 350.70 367.98 5.64 0.371 0.192

35 306.08 330.61 4.18 0.383 0.265

45 252.08 250.12 3.84 0.495 0.297

55 174.07 64.95 3.44 0.60 0.30

The correlation coefficients as presented as a matrix in table 6.3 in order to have an overview of

all parameters together. There a strong association between all the six parameters in general

which indicates a linear relationship. The positive sign means direct relationship while the

negative sign means inverse relationship. What signifies the relationship is how close to 1 (or -

1) the correlation coefficient.

Table ‎0.3 Correlation coefficients between selected parameters.

T

(C)

Relaxation Time

(Sec)

E

(MPa)

Eorigami

(MPa)

E1 1

T (C) 1 -0.992 -0.947 -0.934 0.959 0.914

Relaxation Time (Sec) -0.992 1 0.980 0.890 -0.980 -0.856

E (MPa) -0.947 0.980 1 0.793 -0.980 -0.739

110

Eorigami (MPa) -0.934 0.890 0.793 1 -0.795 -0.988

E1 0.959 -0.980 -0.980 -0.795 1 0.771

1 0.914 -0.856 -0.739 -0.988 0.771 1

Based on the values in table 6.3, the following two relations are proposed where equation (10)

correlates to the experimental data directly, and equation (11) correlates to the Prony series

parameters. Both equations were obtained with the GRG nonlinear solver in Microsoft Excel for

regression.

(10)

(11)

where t and T correspond to the relaxation time and temperature respectively.

These two equations are valid for the tested Miura origami unit cell that has the following

dimensions: unit cell height = 11 mm, folding angle of 90, unit cell element face a = 15.9, and

b= 21 mm.

6.4.3 Unit Cell Deformation and Stress

The viscoelastic model parameters used to simulate the origami unit cell, the relaxation test

results and the obtained parameters of Prony series are used for modeling the unit cell. Figure 6.5

illustrates the stress-strain relation of the simulated origami unit cell; the behavior has the same

trend as in the experimental results with some deviation in the high temperature models from the

values obtained in the experimental test. Figure 6.6 compares the experimental and the finite

element model results of the modulus of elasticity of origami structure, the results show that the

111

values of the elastic modulus were very closed to the values of the experimental ones, and it has

some deviation at 55 C. Figure 6.7 shows the total deformation results of origami unit cell, and

figure 6.8 shows the directional deformation on in Y- direction. The change on the maximum

total and directional deformation was small, while the Von-Mises stress showed a considerable

decrease by the increase of the temperature. Figure 6.9 illustrates the stress distribution of the

four tested models.

Figure ‎0.5 Stress-strain relation of the simulated origami unit cell

112

Figure ‎0.6 Comparison of experimental and FEM model of the modulus of elasticity of origami

model.

Figure ‎0.7 Total deformation of the origami unit cell a) T=25 C, b) T=35 C, c) T=45 C,

d) T=55 C.

113

Figure ‎0.8 Deformation at y direction U2 of the origami unit cell a) T=25 C, b) T=35 C,

c) T=45 C, d) T=55 C.

114

Figure ‎0.9 Von-Mises- stress on origami unit cell a) T=25 C, b) T=35 C, c) T=45 C,

d) T=55 C.

6.4.4 Origami Panel Finite Element Results

Origami panel structure consists of 12 unit cell were simulated using the viscoelastic model

parameters. The panel structure was modeled using ABAQUS viscoelastic model at the four

different temperatures used for the unit cell. Figure 6.10 shows the geometry and the meshed

model of the origami panel. Shell element type was used to simulate the faces of the origami; the

mesh has been refined for accurate results. Figure 6.11 shows the in-plane deformations of the

panel which showing the auxetic behavior of the origami structure, figure 6.11a illustrates the

deformational behavior along the x-axis and figure 6.11b shows the deformational behavior

along the z-axis. The stress strain curves of the origami panels at different temperature is

illustrated in figure 6.12, and figure 6.13 shows the elastic modulus of the origami panel at

elevated temperatures, the modulus dropped to about 40% through the temperature change from

25 C to 55 C.

Figures 6.14-6.16 show the distribution of the total and the directional deformations of the

simulated panel. It is clear that the panel exhibit more deformation by the increase of the

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temperature. Figure 6.17 shows the Von-Mises stress distribution of the four simulated models,

the four models exhibited the same behavior, with high values at the 25 C and lower values at

the 55 C. The maximum stress decreased by 26% at T=35 C, and it decreased by 14% at

T=45 C, and by 9% at T=55 C.

Figure ‎0.10 Origami panel, a) geometrical features, b) meshed model

Figure ‎0.11 The auxetic behavior of the origami panel, a) along the X-axis, b) along the Z-axis

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Figure 6.12 Stress - Strain of origami panel at different temperatures

Figure ‎0.13 Modulus of elasticity of origami panel at different temperatures

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Figure ‎0.14 The total deformation of the origami panel

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Figure ‎0.15 The directional deformation of the origami panel along the X-axis

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Figure ‎0.16 The directional deformation of the origami panel along the Y-axis

Figure ‎0.17 Von-Mises stress generated in the simulated origami panel

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6.5 Conclusion

Origami structure was modeled using a representative unit cell; the unit cell model was simulated

by applying periodic boundary conditions. The purpose of the model is to predict the origami

structure properties by considering the viscoelastic properties. Prony series parameters were

concluded from the experimental stress-relaxation test for the parent material at elevated

temperatures, four different temperatures below the glass transition temperature of the base

material were used to calculate the associated parameters. ABAQUS finite element package was

used to conduct the viscoelastic test of the origami unit cell. Correlation analysis has been done

to predict the correlation coefficients and to give general relation that can be used to predict the

elastic modulus of origami structure based on the viscoelastic properties of the base material.

The work shows the finite element results of the representative unit cell and the origami panel.

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6.6 References

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[3] C. Lv, D. Krishnaraju, G. Konjevod, H. Yu, H. Jiang, Origami based Mechanical Metamaterials.,

Sci. Rep. 4 (2014) 5979. doi:10.1038/srep05979.

[4] M. Eidini, G.H. Paulino, Analysis of Origami-Inspired Structures Computational Science and

Engineering 2014 Annual Meeting, 110 (2014) 3281.

[5] M. Schenk, S.D. Guest, Origami Folding: A Structural Engineering Approach, Origami 5 Fifth Int.

Meet. Origami Sci. Math. Educ. (2011) 1–16.

[6] M. Eidini, G.H. Paulino, Unraveling metamaterial properties in zigzag-base folded sheets, Sci.

Adv. 1 (2015) e1500224–e1500224. doi:10.1126/sciadv.1500224.

[7] M. Schenk, S.D. Guest, Geometry of Miura-folded metamaterials, Proc. Natl. Acad. Sci. 110

(2013) 3276–3281. doi:10.1073/pnas.1217998110.

[8] J.M. Gattas, Z. You, Geometric assembly of rigid-foldable morphing sandwich structures, Eng.

Struct. 94 (2015) 149–159. doi:10.1016/j.engstruct.2015.03.019.

[9] C. Jianguo, D. Xiaowei, F. Jian, Morphology analysis of a foldable kirigami structure based on

Miura origami, Smart Mater. Struct. 23 (2014) 094011. doi:10.1088/0964-1726/23/9/094011.

[10] C. Qiu, V. Aminzadeh, J.S. Dai, Kinematic Analysis and Stiffness Validation of Origami Cartons,

J. Mech. Des. 135 (2013) 111004. doi:10.1115/1.4025381.

[11] N. Wonoto, D. Baerlecken, R. Gentry, M. Swarts, Parametric design and structural analysis of

deployable origami tessellation, Comput. Aided. Des. Appl. 10 (2013) 939–951.

doi:10.3722/cadaps.2013.939-951.

[12] S.H.‎Chróścielewski‎J,‎Makowski‎J,‎Finite‎element‎analysis‎of‎smooth‎folded‎and‎multi‎shell‎

structure.pdf, Comput. Methods Appl. Mech. Eng. 15 (1997) 1–46.

[13] P. Le, European Journal of Mechanics A / Solids Analytical , numerical and experimental study of

the transverse shear behavior of a 3D reinforced sandwich structure, 47 (2014) 231–245.

doi:10.1016/j.euromechsol.2014.04.006.

[14] H. Rahman, R. Jamshed, H. Hameed, S. Raza, Finite Element Analysis (FEA) of Honeycomb

Sandwich Panel for Continuum Properties Evaluation and Core Height Influence on the Dynamic Behavior, Adv. Mater. Res. 326 (2011) 1–10. doi:10.4028/www.scientific.net/AMR.326.1.

[15] A. Lebée, K. Sab, International Journal of Solids and Structures Transverse shear stiffness of a

chevron folded core used in sandwich construction, 47 (2010) 2620–2629. doi:10.1016/j.ijsolstr.2010.05.024.

[16] A. Lebée, K. Sab, Homogenization‎of‎thick‎periodic‎plates :‎Application‎of‎the‎Bending-Gradient plate theory to a folded core sandwich panel, Int. J. Solids Struct. 49 (2012) 2778–2792.

doi:10.1016/j.ijsolstr.2011.12.009.

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[17] A. Lebée, K. Sab, Comptes Rendus Mecanique Homogenization of cellular sandwich panels,

Comptes Rendus Mec. 340 (2012) 320–337. doi:10.1016/j.crme.2012.02.014.

[18] E. Baranger, P. Guidault, C. Cluzel, Numerical modeling of the geometrical defects of an origami-

like sandwich core, Compos. Struct. 93 (2011) 2504–2510. doi:10.1016/j.compstruct.2011.04.011.

[19] E.A. Peraza, D.J. Hartl, E. Akleman, D.C. Lagoudas, Computer-Aided Design Modeling and

analysis of origami structures with smooth folds ✩, Comput. Des. 78 (2016) 93–106.

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[20] W. Wu, J. Owino, A. Al-ostaz, L. Cai, Applying Periodic Boundary Conditions in Finite Element Analysis, (n.d.) 707–719.

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Chapter 7.

Conclusion and Recommendations

7.1 Concluding Remarks

In Order to develop polymeric origami cores for load and energy dissipation, this research the

focus of this research was in the development, characterization, and modeling of origami

structure cores. Two types of origami tessellation patterns were considered in the research,

Miura, and Ron- Resch-like origami structures. The work adopted the pre-folding process to

fabricate origami panels, to eliminate any overlap or interfere of the unit cell facets.

Origami metamaterial can offer many benefits to many engineering applications, most

importantly high stiffness, high energy absorption efficiency, and light-weight. Miura Origami

structures are fabricated in by direct molding of the geometrical features from PLA and TPU

polymeric blends. Direct molding avoids the defects related to a conventional folding of flat

sheets when typically making origami structures. The following blends were fabricated for

PLA/TPU (100/0, 80/20, 65/35, 50/50, 20/80, and 0/100). These different percentages of PLA

and TPU reflect the increase in compressive strength or energy transfer respectively. The balance

between PLA and TPU will depend on the intended application. PLA origami structure offers

maximum force transfer of 686.1 N and highest compressive modulus of 4.6 MPa. The high

compressive modulus of PLA resulted in fracture at crease lines. The high modulus of PLA

origami structure can be reduced to 2.79 MPa by adding 35% of TPU which offers more

elasticity and avoid failure at high compressive strains. The addition of 35% TPU also reduces

the force transfer to 2.8 KN. The finite element modeling has been conducted using static

structural for compression test and explicit dynamics for impact event. The compression results

showed that the crease lines are the stress concentration zones, and it is subjected to fracture in

the blends with high elastic modulus while the faces carry low-stress values. The FEA results

also demonstrated that origami made structure made of a high percentage of 80% TPU has the

highest values of energy absorption (up to 3.3 J), with directional deformation exceeded (1.6

mm), and it has the lowest Von-Misses stress in compression. This work provided numerical

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quantification of the compromise between compressive strength and energy transfer which can

be used to design origami structure with target values for both.

The way the origami metamaterial can redistribute compression and impact forces make it

qualified for potential use in future applications, as a light-weight sandwich core. The use of

CNF with the material blends to fabricate composite origami structures significantly enhances

the overall mechanical properties of the origami cores in compression, in which the compressive

modulus and the strength of the origami cores were increased by the increase of the CNF. By

noting that samples with high PLA content face fracture through the crease lines, while low PLA

samples showed more elastic behavior. The impact testing showed a higher transferred force and

energy for higher carbon nanofiber compositions, because of the increasing in the rigidity of the

samples. 65PLA/35TPU showed the highest transferred force because of the coupling effect of

rigidity, flexibility and fiber reinforcement, while the higher PLA composition samples showed

major brittle behavior and the lower PLA composition samples showed flexible behavior. The

DSC test results showed an improvement in glass transition for both TPU and PLA with the

increasing amount of CNF, and the DMA results showed a significant increasing of the storage

modulus and a slight improvement of the loss modulus. Active composite origami structures

showed fractures along crease lines and low recovery ratio, composite origami with low CNF

percentages (0.1%) showed good stress relaxation behavior and high recovery ratio.

Advances in designing and investigating origami-inspired materials can lead to the production of

materials with properties that can be used in a wide range of applications that require high loads

and energy damping. In this work, Ron-Resch-Like flat origami panels were fabricated by 3D

printing, and the material used was PLA filaments. The fabricated samples were tested in

compression and impact. The impact results revealed that the Ron-Resch-Like cores have

advance for damping impact forces and dissipating energy compared with Miura origami cores.

However, the Ron-Resch-like cores exhibited a single fracture in the tip of the star tuck. Fused

deposition modeling can be used to fabricate such complex origami configurations. Different

Ron-Resch configurations should be characterized and compared to optimize the best

geometrical parameters. Optimization and finite element simulation should be conducted to

compare the parameters of the designed cores. It is important to design ink material for 3D

printing that can be used with 3D printers for different applications.

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Origami structure was modeled using a representative unit cell; the unit cell model was simulated

by applying periodic boundary conditions. The purpose of the model is to predict the origami

structure properties by considering the viscoelastic properties. Prony series parameters were

concluded from the experimental stress-relaxation test for the parent material at elevated

temperatures, four different temperatures were used to calculate the associated parameters.

ABAQUS finite element package was used to conduct the viscoelastic test of the origami unit

cell. Correlation analysis has been done to predict the correlation coefficients and to give general

relation that can be used to predict the elastic modulus of origami structure based on the

viscoelastic properties of the base material.

7.2 Major Contributions

In this thesis, five major studied were introduced in order to achieve the objectives of the

research. The contributions of these studies were in the design, characterization, fabrications, and

modeling of origami structure panels. The following are the descriptions of the major

contributions of the thesis:

1- Using multi-phase polymeric materials to fabricate pre-folded origami cores by using

compression molding process. The mold designed in a way that can produce the

complicated origami features directly to the fabricated panels, and avoiding the

folding process. Miura origami pattern was the studied pattern due it is unique design

and easy way to fold and unfold during the loading stage. The material effect on the

origami structures has been tested by using 6 different material blends compositions.

The selected material was PLA and TPU, and the produced blends have been

characterized by studying the thermal and viscoelastic behavior of the material

blends. Finite element package was used to simulate the static and the explicit

dynamics behavior of the cores.

2- To improve the mechanical stiffness of origami pattern, CNF was added as filler to

multiphase polymeric blends, the percentages of the CNF were 1%, 3%, and 5 %.

Miura origami panels were fabricated using molding process. The passive and the

active properties were investigated in terms to study the energy dissipation efficiency

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of the designed cores, and to see the shape recovery of the deformed origami

structure.

3- For optimizing the geometrical features of Ron-Resch-like origami patterns were

studied. The study investigated 9 different Ron-Resch-like origami patterns, three star

tuck branches, four star tuck branches, and six star tuck branches, with three different

angles 15, 30 and 60. Fused deposition modeling was used to fabricate the pre-

folded Ron-Resch-like panels. Simulations using finite element solvers were

performed for compression and impact tests and compared with the experimental

results. A unit element from each design tested for the shape memory effect, which

showed high shape recovery ratio. The designed panels showed high efficiency in

impact performance compared with other types of cores.

4- Lastly, Modeling of origami structures using representative unit cell by considering

the viscoelastic properties of the parent material was introduced. The model used

periodic boundary conditions for the repeated unit cell. Relaxation moduli were

measured in four different temperatures. The coefficients of the Prony series then

calculated and used for the viscoelastic model of the ABAQUS package. Empirical

equations were provided to predict the elastic modulus of the origami structure as a

function of temperature.

7.3 Recommendations

Origami structures have the ability to be used effectively for load dissipation and energy

damping. Conventional sandwich cores still suffering from many drawbacks and it has been used

for decades for compression and impact applications, replacing origami structures with

conventional cores can compensate its limitations. More geometrical designs origami can be

studied in order to optimize the best patterns for the target applications. Controlling the

connectivity of origami unit cells and the unit cell faces can provide controllable origami

structures and enhance the final properties. The vast advance of the manufacturing technology

can be utilized to fabricate more complicated origami patterns for high end applications. More

investigations on the viscoelastic properties can add accurate predictions of the mechanical

behavior of the designed polymeric origami structures. Developing new origami tessellations can

be done by utilizing CAD systems, or by using origami patterns generators software, such tools

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can add more details for the tessellation in which can be a good way of enhancing the target

properties. For highly effective design, two important factors should be taken in consideration:

the connectivity between the facets of the unit cell and the overlapping degree between unit

cells’ elements. The design of experiment DOE, is one of the tools that be used in the case of

including large number of design parameters in the experiments, it is the way to find the

parameter sensitivity. In our case DOE is not strongly applicable in our case in which fixed some

parameters and working with the other parameter. Such as the main parameters that affect the

system are material parameters, in the first and second studies, and in third study we fixed the

material and investigated the geometrical parameters. Based on the size of the parameters date,

the DOE can be addressed in future work. In the average of the results in study 1 as shown in

figures 3.11 and 3.12, show that the energy transferred is related to the force transferred, as we

can see in figure 3.10 that shows the impact force transferred, the clear change which gives

confident‎about‎the‎obtained‎results‎of‎the‎energy‎transferred,‎that’s‎what‎let‎us‎confidently‎trust‎

the results by just considering the standard deviation and no need to use another statistical tool,

which is recommended in the case of large experimental data results. To address the issue of

fabrication of origami structures, advanced manufacturing techniques such as fused deposition

modeling, can be developed for printing and folding processes in a combined process. By

tailoring the viscoelastic and mechanical properties of the polymeric blends, the structural

performance of the origami structures can be enhanced to satisfy the requirements of high-end

applications. Modeling of polymeric origami structures by using powerful tools, and by

considering the detailed features of the origami structures, and the detailed viscoelastic

properties of the base material can predict the exact properties and reduce the cost of the design.

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