Magneto-Active Elastomers

Multi-Field Responsive Origami Structures Faculty: Mary Frecker, Zoubeida Ounaies, Tim Simpson, Paris von Lockette, Jyh-Ming Lien, Rebecca Strzelec

Pennsylvania State University &

George Mason University

Micro-Scale Meso-Scale Macro-Scale

Project Overview

The EFRI-ODISSEI project aims to develop multi-field actuated origami structures that achieve folding and unfolding from a flat state to a complex, artistically inspired, 3D geometry. This work encompasses a multi-scale approach, ranging from frameworks based on material microstructure to the macroscopic 3D analysis of foldable structures. Each length scale contributes to the goal of this project by providing essential information only available at that level.

At the micro-scale, the effects of microstructure on the coupling properties of active materials are determined. For example, the squareness ratio of MAEs (saturation magnetization over remanent magnetization) is found to be dependent on volume concentration of barium hexaferrite.

Modeling Bending/Folding

25.0MV/m 37.5MV/m 62.5MV/m 56.2MV/m

H

M

� α

�sin(α)

M

H

�

�

(a) (b)

Electro-Active Polymers

The bifold folds up in experiment.

The simulated deformation for a quarter of bifold structure.

Surface load � to simulates magnetic torque

Optimal Solution

Blood Perfusion

Electrical Conductivity

Thermal Conductivity

Constant properties

Effect of temperature dependent material properties

Radiofrequency Ablation for Abdominal Tumors

FE Modeling of Notched Unimorph

Analytical Modeling for Multi-Layers

� =����

������ �� =

����

�� =����

EAP: P(VDF-TrFE-CTFE) Adhesive Electrode Passive substrate

Multi-layered composite

Radius of curvature: Strain at y = 0 axis: e0

Cleared spot Breakdown spot

70 MV/m 100 MV/m

Project Overview

...

...

Unfold

Orignial meshAssemble

Overlapping analysis

Failed to fold

ClusteringSegmented mesh

UnfoldFailed to unfold

Fold

NetsContinuous folding

Mathematics of Folding

We gratefully acknowledge the support of the National Science Foundation EFRI grant number 1240459 and the Air Force Office of Scientific Research.

0 MV/m

30 MV/m 35 MV/m 40 MV/m 50 MV/m

Magnetically-Actuated Structures

The box configuration starts flat and achieves folding on the edges

The bifold starts from a flat state and folds under an applied magnetic field. This is simulated in COMSOL by coupling the magnetics module with the solid mechanics module.

Field strength increases

Students: Anil Erol, Wei Zhang, Saad Ahmed, Brad Hanks, Corey Breznak, Katherine Reichert, Logan Althoff, Landen Bowen, Brett Cowan, Zhonghua Xi, Sarah Masters, Erika Arrojado

-150

-100

-50

0

50

100

150

-25000 -20000 -15000 -10000 -5000 0 5000 10000 15000 20000 25000

Mag

net

izat

ion

(em

u/g

*)

Field Strength (Orsteds)

10% 15% 20% 25% 30% 35%

Magnetic Actuation Based on Hard Magnetics

Self-Clearing Increases Breakdown Field

Resin Pools

Magnetically aligned Resign Pool

The meso-scale bridges the micro- and macro-scales. An example of this is the Multi-Material DLP printer, which prints arbitrarily poled magneto-active materials in 3D; thus, the printer applies microsctructural alterations on large , complex structures

Electric Actuation: Dipole Interaction Based Electrostriction

Relaxor Ferroelectric Polymer Film of P(VDF-TrFE-CTFE) Amorphous region

Nano-polar region

��� ���

��� V

Barium Hexaferrite Particle Alignment

Magnetization hysteresis curves for varying volume fractions of barium hexaferrite in a PDMS matrix

A single particle is modeled as a discrete dipole

�′�,��� = �′[sin�′ sin�′ ,sin�′ cos�′ , cos�′ ]

• �′ and �′: azimuthal and polar angles (with respect to a cluster’s orientation, �� = ��� ,��� ,��� )

• ��: strength (magnitude) of dipole

The population of dipoles have an orientation-averaged moment density value Random � = 1/3 Aligned � = 0

���

���

���

��

��

< �′��, ��, �� > =���� �′; ���, ��� ��� �; ���, ��� ��� �′ ; ���, ��� �′�′,�′, �′ ����

�,�

Folding/Curling of Notched Samples

� = ���������� +������������ RVEs Constructed Based on Dipole

Orientations ����������� =

1

4��

�� ⋅ ����

−3 �� ⋅ ��� �� ⋅ ���

�� ����������� = �����

1

���

���

��� − 3�

�

���

Eight-chain hyperelastic model Dipole-dipole interaction energy

2. Multi-chain, a central dipole interacts with a probability distribution (PDF) of dipole densities

� �| �,� =��

����� ���� ���

2��

1. Single chain, in which two dipoles interact, connected via an elastic chain

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

No

rmal

ized

Neg

ativ

e St

rain

E (MV/m)

Single Horizontal

Single Vertical

PDF - Horizontal

PDF - Vertical

Non-dimensionalized model compares single chain versus PDF approximations

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

-Str

ain

No

rmal

ized

E (MV/m)

PDF parameters are explored

�� increases

0

0.5

1

1.5

2

2.5

3

3.5

0 2000 4000 6000 8000 10000

-Str

ain

(%

)

E2 (MV/m)2

σ1 = 0.8 Experiments

C�

(GPa)

�� �� ��

�

�� �� ����

(MV/m)

P(VDF-TrFE-CTFE) 150 2.5 8 0.08 0 25

Microstructure-Based Electrostriction Model

Conclusions

Trade space visualization

Multi-field simulations of a bimorph are developed by implementing electromechanical and magnetic constitutive equations into a 1D boundary value problem in which large deformations are achieved via Euler-Bernouilli beam equation

Notched unimorphs are modeled in COMSOL by shell elements, in which applying a pressure in the active layer simulates electrostriction

Shape Modeling International (SMI) 2016, also in Computer & Graphics [Xi and Lien]

0.5

0.6

0.7

0.8

0.9

1

0.05 0.15 0.25 0.35

Sq

ua

ren

ess

Volume Concentration of BHF

Re-config

Bunny-2206 Fish-2206

Each length scale provides vital components for a multi-field actuated Origami product. Material characterization is transferred into the meso-scale

to generate constitutive relations that are applied to 1D composite bending/folding, building a foundation for more complex 3D structures such

as transformers via stacking. Ongoing work involves the optimization of composite geometries and material configurations in simulations to achieve

target shapes for specific Origami applications