Multiscale Material Modeling with Multiscale Designer Material Modeling with Multiscale Designer...

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Multiscale Material Modeling with

Multiscale Designer

Jeff Wollschlager

Sr. Technical Director

(425) 949-9674

[email protected]

mailto:[email protected]

Copyright © 2013 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.

Who is the Multiscale Designer team?

Jacob Fish (New York, NY)

Founder Multiscale Design System (MDS)

Professor at Columbia University; Remains as Chief Scientific Advisor to Altair

Zheng Yuan (Beijing, China)

Principal Multiscale Designer Developer

Robert Crouch (Nashville, TN)

RADIOSS, LS-DYNA, and Abaqus Solver Interface Expert

Colin McAuliffe (Hoboken, NJ)

Multiscale Designer Expert and Developer

Dimitrios Plakomytis (Paris, France)

Multiscale Designer Developer

Jeff Wollschlager (Seattle, WA)

Multiscale Designer Program Management, Business Development, and Developer

mailto:[email protected]?subject=Multiscale Designer Question







What does Multiscale Designer do?

Development of Multiscale Material Models from the Linear Regime to

Ultimate Failure and Application of those Models in Finite Element Analysis

Example Unidirectional Carbon Fiber Reinforced Plastics (CFRP)

Scale 1 – Fiber/Matrix

Scale 0 – Constituent Microstructure

Matrix Fiber

Scale 3 – LaminateScale 2 – Lamina/Ply


Another Multiscale Example

Five Harness Satin (5HS) Weave CFRP



Scale 3 – Woven Ply (5HS)

Scale 2 – Tow

Matrix Fiber

Scale 4 – Laminate


Another Multiscale Example

Metals (Steel, Aluminum, Titanium)

Scale 1 – Homogenized Steel, Aluminum, Titanium

Scale 0 – Constituent Microstructure (Grain Boundaries)

***For metals we perform simulations at Scale 1***

***One scale away from the Constituent Microstructure***


What does Multiscale Designer do?

Development of Multiscale Material Models from the Linear Regime to

Ultimate Failure and Application of those Models in Finite Element Analysis

Example Unidirectional Carbon Fiber Reinforced Plastics (CFRP)



Matrix Fiber

Scale 3 – LaminateScale 2 – Lamina/Ply


Why do we need Multiscale Modeling?

Example Open Hole Tension (OHT) Specimen

• 8 plies of unidirectional CFRP

• 0.5” diameter (D)

• 3” width (W/D = 6)

Modeling at the Laminate Scale 3

• Model “as-if” one material

known as “Black Aluminum” Designs

• Laminate stiffness E lam

represent average stiffness of all plies

• Laminate stress s lam

represents average stress over all plies

• Allowables written at the laminate scale

• Changes in single ply cause allowable changes

• Current modeling standard in Production Environments

Scale 3 - Laminate



Modeling at the Ply Scale 2

• Ply stiffness E ply

represent average stiffness of all fibers/matrix

• Ply stress s ply

represent average stress over all fibers/matrix

• Allowables written at the ply scale

• Changes in fiber/matrix cause allowable changes

• Current modeling standard in R&D Environment

PROBLEM

• Ply scale not sufficient to predict material behavior,

need Scale 1 to predict material behavior

SOLUTION

• MultiScale methods

Scale 3 - Laminate

Scale 2 - Ply



Modeling at the Fiber/Matrix Scale 1

• Constituent stiffness Efiber Ematrix

• Constituent stresses sfiber & smatrix

• Allowables written at the constituent scale

• Current modeling standard by Early Adopters

PROBLEM

• Can not explicitly model at the fibers/matrix scale

SOLUTION

• MultiScale methods transform sply sfiber & smatrix

• Now we can predict material behavior!!

𝜎𝑝𝑙𝑦

𝜎𝑓𝑖𝑏𝑒𝑟

𝜎𝑚𝑎𝑡𝑟𝑖𝑥

𝐸𝑝𝑙𝑦

𝐸𝑓𝑖𝑏𝑒𝑟

𝐸𝑚𝑎𝑡𝑟𝑖𝑥

Predict Material Behavior

Scale 2 - Ply



Multiscale Designer Work Flow

1. Develop a Multiscale Material Model for material of interest

2. Populate the Material Database with necessary material parameters

3. Develop a Homogenized FEA Model which interacts with

Material Database for material properties

4. Export a FEA Model and Solve

Material

Database

1

2

3

4

4


Altair HyperWorks Multiscale Designer


Multiscale Material Model Development Methodology

Step 1

• Unit Cell Model Definition

Step 2

• Linear Material Characterization

• Forward Homogenization

• Inverse Optimization

Step 3

• Reduced Order Model

• Provides Computational Efficiency to multiscale simulations

• Database of Material Properties

Step 4

• Nonlinear Material Characterization

• Forward Homogenization

• Inverse Optimization


Step 1 - Unit Cell Model Definition

Fibers

Particles

Weaves

Random Inclusions

Square Square w/ Interphase Hexagonal Hexagonal w/ Interphase

Cubic Cubic w/ Interphase BCC BCC w/ Interphase

Plain Weave 4 Harness Satin 5 Harness Satin 8 Harness Satin

2D Chopped Fiber 3D Chopped Fiber Ellipsoids Spherical


Step 2 - Linear Material Characterization

Forward Characterization

Inverse Characterization

Many times E fiber is not known but E ply and E matrix are known from test

Linear

Regime

Nonlinear Regime

Damage Law

Ultimate

Failure

Strain

Str

ess (

psi)

initial valuescalculate

new valueserror from

measured values

Optimization

Loop

measured values

Ehomogenized Ematrix Efiber

EhomogenizedEmatrix Efiber+ =


Step 3 - Reduced Order Model (ROM)

PROBLEM

Solving FEA unit cell models at every element gauss point for every nonlinear iteration

is computationally expensive and unrealistic with todays computer power

SOLUTION

ROM obtains FEA unit cell results accuracy with analytical efficiency

Reduced

Order

Model

s,e ply

E ply

Inefficient FEA Unit Cell Calculations Efficient Reduced Order Model Calculations

s,e ply

s,e fiber s,e matrix E fiber E matrixs,e fiber s,e matrix E fiber E matrix

E ply


Example of a Reduced Order Model (ROM)

𝜎 = 𝐶 𝜀 𝜎 𝑚 = 𝐶 𝑚 𝜀 𝑚 𝜎 𝑓 = 𝐶 𝑓 𝜀 𝑓

𝜎 = 𝜎 𝑚𝑉𝑚 + 𝜎 𝑓𝑉𝑓

𝜀 = 𝜀 𝑚𝑉𝑚 + 𝜀 𝑓𝑉𝑓

𝐶 𝜀 = 𝐶 𝑚 𝜀 𝑚𝑉𝑚 + 𝐶 𝑓 𝜀 𝑓𝑉𝑓

𝐶 𝜀 = 𝐶 𝑚 𝜀 𝑚𝑉𝑚 + 𝐶 𝑓 𝜀 − 𝐶 𝑓 𝜀 𝑚𝑉𝑚

𝐶 𝑚 − 𝐶 𝑓 𝜀 𝑚𝑉𝑚 = 𝐶 − 𝐶 𝑓 𝜀

𝜀 𝑚 =1

𝑉𝑚𝐶 𝑚 − 𝐶 𝑓 −1

𝐶 − 𝐶 𝑓 𝜀

𝜀 𝑚 = 𝑀 𝑚 𝜀

𝜎 𝑚 = 𝐶 𝑚 𝑀 𝑚 𝜀

𝜀 𝑓 = 𝑀 𝑓 𝜀

𝜎 𝑓 = 𝐶 𝑓 𝑀 𝑓 𝜀

𝜀

Homogenized Material Matrix Material Fiber Material

Matrix Material Fiber Material

ROM


Step 4 - Nonlinear Material Characterization

Each phase characterized with one continuum damage law

Isotropic Continuum Damage

• Bilinear Damage Evolution

• 3-Piecewise Damage Evolution

Orthotropic Continuum Damage

• Bilinear Damage Evolution

• 3-Piecewise Damage Evolution

Rate-Independent Plasticity

Hybrid Isotropic Damage & Plasticity

Viscoplasticity

Keep Elastic

Virtual Testing/Allowables for the following specimens

1. Unnotched Tension/Compression

2. Open Hole Tension/Compression

3. 3-Point Bend (Short Beam Shear)

4. 4-Point Bend

5. Rail Shear

Nonlinear Regime

Damage Law

Linear

Regime

Ultimate

Failure

Strain

Str

ess (

psi)


NIAR AGATE T700/2510 Unidirectional Material

All Presented Multiscale Designer Comparisons vs. Measured Data from

NIAR AGATE Report and Toray Composites (America) Report;


Step 1: Unit Cell Model Definition (Tension & Compression)

T700/5210 Uni Physical Properties

FAW = 150 g/m2

rf = 1.79 g/cm3

CPT = 0.0060 in

𝑉𝑓 =25,400 ∗ 𝐹𝐴𝑊

𝐶𝑃𝑇 ∗ 𝜌𝑓= 0.545 (54.5%)

Hexagonal Pack Unit Cell

Avg. Element Size 0.05 in x-strain, x-stress y-strain, y-stress


Step 2: Linear Material Characterization (Tension)

Experimental Data Required to

Develop a Unidirectional Product Form Multiscale Material Model

0-Tension ASTM 3039

90-Tension ASTM 3039

0-Comperssion ASTM 6641 (only if need compression behavior)

90-Compression ASTM 6641 (only if need compression behavior)

[45/-45] Tension ASTM 3518


Step 2: Linear Material Characterization (Tension)

initial valuescalculate

new valueserror from

measured values

Optimization

Loop

measured values

Ehomogenized Ematrix Efiber

Linear

Regime

Nonlinear Regime

Damage Law

Ultimate

Failure

Strain

Str

ess (

psi)

Fiber

Matrix

Properties

Inverse

Optimization

Initial Values

Inverse

Optimization

Results (Msi)

Em,t 0.550

(est. value)

0.550

nm 0.36

(est. value)

0.36

E1f,t 34.80

(high value)

32.97

E2f,t n/a 0.257

n12f n/a 0.2725

n23f n/a 0.30

G12f n/a 0.475

Homogenized

Properties

Multiscale Designer

Homogenized

Results (Msi)

Measured

Values (Msi)

E1t 18.210 18.209

E2t 1.219 1.219

n12 0.309 0.309

n23 0.444 n/a

G12 0.613 0.613

G23 0.422 n/a

Fiber & Matrix Linear Properties Homogenized Linear Properties

Inverse Optimization


Step 4: Nonlinear Material Characterization (Tension)

Nonlinear

Property

How

Obtained?

Property

Value (psi)

K0m Inverse Optimization

from t v g

6,910

K1m Inverse Optimization

from t v g

16,850

dm Inverse Optimization

from t v g

29.25

Hm Inverse Optimization

from t v g

8,350

S0m,t

(Mean

Stress)

90-Tension

Matrix Stress Calculation

2931

E1m,t

(Volumetric

Strain)

90-Tension

Matrix Strain Calculation

0.00492

𝜀 𝑚 = 𝐴_𝑛 1 𝜀

𝜎 𝑚 = 𝐶 𝑚 𝜀 𝑚

Em

Hm

K0m

K1m

dm

E2

S0 (Mean Stress in Matrix)

E1

(Volumetric Strain in Matrix)

E0 (Volumetric Strain in Matrix)

Nonlinear

Property

How

Obtained?

Property

Value (psi)

S01f,t 0-Tension

Fiber Stress Calculation

570,331

(ef = 1.72%)

E11f,t 0-Tension

Fiber Strain Calculation

0.019

(1.9%)

S02f,t 90-Tension (min value)

Fiber Stress Calculation

57,000

E12f,t 90-Tension (min value)

Fiber Strain Calculation

0.0243

(2.43%)

E1E0

(Strain in Fiber)

(Stress in Fiber) S0

Matrix Tension

or

[45/-45] Tension

90-Tension 0-Tension

𝜀 𝑓 = 𝐴_𝑛 2 𝜀

𝜀 𝑓 = 𝐴_𝑛 2 𝜀

𝜎 𝑓 = 𝐶 𝑓 𝜀 𝑓

𝜎 𝑓 = 𝐶 𝑓 𝜀 𝑓

Matrix Nonlinear Properties Fiber Nonlinear Properties


Multiscale Material Model Development Methodology

At this point a complete multiscale material model for T700/2510 has been

developed from;

• 0-Tension

• 90-Tension

• 0-Compression

• 90-Compression

• [45/-45] Tension

All validation simulations forward simply apply the multiscale material model

developed above coupled with parametric FEA models generated and solved

automatically by Multiscale Designer!

• UNT, UNC, OHT, OHC

• [50/40/10], [25/50/25], [10/80/10]

In addition, the multiscale material model can be used in any 3rd party macro solver;

• OptiStruct (v2017 or later)

• RADIOSS (v14.0 or later)

• Abaqus (v6.13 or later)

• LS-Dyna (R8.0.0 or later)


Laminate Stacking Sequences

[%0 / %+/-45 / %90]

[50/40/10]

[45/0/-45/90/0/0/45/0/-45/0]s

20 plies

[25/50/25]

[(45/0/-45/90)3]s

24plies

[10/80/10]

[45/-45/90/45/-45/45/-45/0/45/-45]s

20 plies


Multiscale Designer Validation Overview


Using the Multiscale Material Model in Macro Solvers

Multiscale

Designer

User Defined

Material (dll)

RADIOSS

OptiStruct


Multiscale Designer Stochastic

Probabilistic vs. Deterministic Simulation of Multiscale Designer Mechanical

Enter all values as Distributions (Mean, Standard Deviation) vs. Single Value

Virtual Allowables generation supported by Test (i.e. A- B-basis calculations)


Multiscale Designer Fatigue

Similar process to Multiscale Designer Mechanical

Fatigue Law vs. Failure Law of Multiscale Designer Mechanical

Virtual Fatigue Allowables generation supported by Test


What documentation exists?

User Manual Theory Manual

(access from product) (available on Amazon or Other)


Let us know how we can help you!

Jeff Wollschlager

Sr. Technical Director

(425) 949-9674

[email protected]

mailto:[email protected]

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