2008 international ansys conference international ansys conference multiscale cae system for ... •...

© 2008 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

2008 International ANSYS Conference

Multiscale CAE system for wide field problems

Mr. Koji YamamotoApplication EngineerCYBERNET SYSTEMS CO.,LTD.


Table of Contents

1. Motivation

2. Functions of Multiscale CAE system

4. Demonstration

5. Summary and future plan

Technical issues and application example of Multiscale CAE system

Homogenization, macro, localization analysis

3. TheoryNumerical material testing

Example for structural multiscale analysis


Motivation

Computational chemistry Computational mechanics

Computational material sciencesquantum nano micro meso macro

Structural dynamicsPolycrystalline elasticity

l t l ti itMolecular dynamics

Quantum mechanics

quantitativequalitativeCollectivity of molecular

Structure

Traditional CAEExpanded CAE

10010-310-610-910-12

……………..


• Application Example 1(Development for new composite materials ）– Examination for FRP property.

Strand angleExamination for filament section shape

Examination for matrix material

Technical issues for Multiscale Analysis

Not efficient, both costs & time wise, to examine for all cases.

to simulate by ANSYS(w/oMultiscale)?Efficient

Macro scale Micro scale

…[m]

>>The analysis (without Multiscale) is not always reasonable choice.

to involve micro scale model into macro scale ?

[ Is it reasonable …]

to replace homogeneous media by using material constant for micro scale ?

NO, it can cause staggering high number of node.

NO, it absorb the micro scale results.


• Application Example 2 (Cut down on Analytical model scale）– Fluid flow in cylinder with barrier

Porous mediaFluid

Technical issues for Multiscale Analysis

Macro scale

Micro scale

Difficult to include micro scale shape into macro scale model.

Homogenize a micro scale shape by applying permeability or loss coefficient.


Function of Multiscale CAE System

• Function of Multiscale CAE system 1 : Homogenization Analysis– Homogeneous material properties are evaluated from

numerical material testing of micro unit cell which is assumed to be cyclic symmetry with every direction.

Homogeneous material parameter (Ex,Ey,Ez,Prxy,etc…)

Micro scale model Unit cell Macro scale model

Numerical material testing (uniaxial tensile, Pure shearing etc…)



• Analysis function– Homogenization Analysis

• Structural ：Elastic moduli,Poisson's ratios, Shear moduli• Thermal ：Thermal conductivity, Specific heat• Seepage ：Permeate coefficient• Current ：Electrical resistivities • Electric ：Electric relative permittivity• Magnetic ：Magnetic relative permeability • Other ：Density, Thermal expansion

• Convenience of Homogeneous analysis• Reduce the cost of time and material for testing.• Provide ideal testing environment.



• Function of Multiscale CAE system 2.– Macro scale analysis

• Non-Homogeneous model is assumed to be homogeneous one by using equivalent material parameter evaluated by homogeneous analysis.

Assuming equivalent homogeneous media.

It is not realistic to make and analyze a macro scale model with microstructure.

Each element take over the properties for unit-cell



• Function of Multiscale CAE system 3.– Localization analysis

• Result distributions in micro scale is obtained from macro analysis results.

Macro analysis result Localization analysis result

Specific element you want to localize is selected. Sub-structuring is executed.

Localized

homogenized localizedmicro micromacro

Summary of Multiscale function


Multiscale CAE System

• Multiscale CAE System GUI (ANSYS Classic)


Multiscale CAE System

• Multiscale CAE System GUI（ ANSYS Workbench）


⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣ

12

22

11

333231

232221

131211

12

22

11

2EEE

CCCCCCCCC

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣ

31

21

11

333231

232221

131211

)1(12

)1(22

)1(11

00

CCC

EE

CCCCCCCCC

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣ

32

22

12

333231

232221

131211

)2(12

)2(22

)2(11

0

0

CCC

EECCCCCCCCC

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣ

33

23

13

333231

232221

131211

)3(12

)3(22

)3(11

00

CCC

EECCC

CCCCCC

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣ

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

)1(12

)1(21

)1(11

31

21

11 1E

CCC

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣ

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

)2(12

)2(21

)2(11

32

22

12 1E

CCC

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣ

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

)3(12

)3(21

)3(11

33

23

13 1E

CCC

EC H=Σ

1)

2)

3)

CH

Constitutive equation for macro scale

Theory : Homogenization analysisIdentification of homogenized elastic matrix

y1

y2

CA

CB


Theory : Homogenization analysisNumerical material testing

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

00)1(

EE

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

0

0)2( EE

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧=

EE 0

0)3(

Forced displacement

σ2

σ2

σ1

σ1

Macro stress (Σ) is evaluated from reaction force of face (micro stress σ)

∫ ⋅∂

=Σ dyeY ji

iij σ1

y1

y2


Analysis example for 2D model

{ }TE 001)1( = { }TE 010)2( = { }TE 100)3( =

{ }T04401475)1( =Σ { }T01836440)2( =Σ { }T102600)3( =Σ

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧

ΣΣ

4400

)1(22

)1(12

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧

ΣΣ

18560

)2(22

)2(12

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧

ΣΣ

01026

)3(22

)3(12

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧

ΣΣ

10260

)3(12

)3(11

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧

ΣΣ

0440

)2(12

)2(11

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧

ΣΣ

01475

)1(12

)1(11

{ }TE 001)1( =

{ }TE 010)2( =

{ }TE 100)3( =

{ } { }T04401475)1(12

)1(22

)1(11

)1( =ΣΣΣ=Σ

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

ΣΣΣΣΣΣΣΣΣ

=⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

=102600

0185644004401475

)3(12

)2(12

)1(12

)3(22

)2(22

)1(22

)3(13

)2(12

)1(11

333231

232221

131211

HHH

HHH

HHH

H

CCCCCCCCC

C

{ } { }T01856440)2(12

)2(22

)2(11

)2( =ΣΣΣ=Σ

{ } { }T102600)3(12

)3(22

)3(11

)3( =ΣΣΣ=Σ

CH : Homogenized elastic stiffness matrix


Theory : Macro Analysis

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

1026000185644004401475

HC

Micro scale

Macro scale Model

Macro CAE

Macro Analysis result

Homogenized

….….Specific element you want to localize is selected. The averaging strain (E) is taken over to localization analysis by using element table.

3105.02.0

0.1−×

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧−=E

Micro CAE


Theory : Localization Analysis

{ } 3105.02.01 −×−= TEMacro strain of selected element (E)

3

22

12 102.0

5.02 −×⎭⎬⎫

⎩⎨⎧−

=⎭⎬⎫

⎩⎨⎧

EE

3

12

11 105.0

12

−×⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧

EE

Boundary condition for localization

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧ΣΣ

0696.0257.0

22

12

⎭⎬⎫

⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧ΣΣ

257.039.1

12

11

EC H=Σ { }T257.00696.039.1=Σ

Localized stress and macro stress

is equal to stress of macro analysisΣ


Demonstration

55 deg

30 deg

X direction

X direction

Macro modelInner pressured cylinder (1/4 cyclic)

X direction

Which is the proper configuration to make up cylinder ?

Micro model30 and 55 degree blade model


Demonstration : Macro scale analysis


Localization analysis results

<30 degree blade model>Max. equivalent stress 195.166 [MPa]Min. equivalent stress 27.314 [MPa]

<55 degree blade model>Max. equivalent stress 104.905 [MPa]Min. equivalent stress 37.143 [MPa]


Summary and future plan

Three functions for multiscale CAE system (homogeneous, macro, localize analysis ) has been built into ANSYS GUI.

Multiscale analysis example have been demonstrated for cylinder structural model.

As the next step, Multiscale CAE system will upgrade to be able to analyze non-linear problem.

Homogeneous for…PlasticityHyper elasticityVisco elasticityCreep

material property

Localization for…large strainlarge deflections

analysis


Future plan 1: Nonlinear homogenization

X_tensile Y_tensile Z_tensile

Material testing results

Homogeneous analysis function will be expanded for non-linear material property.

Homogeneous material constants is identified. (TB,CREEP or TB,KIHN with TB,HILL etc..)

homogenized

you can choose many kinds of testingUniaxial tensile/compressionEquibiaxial tensile/compressionCyclic loadStress relaxation

you can evaluate many kinds of output

Stress-Strain curveStress-time curveStrain-time curve


Future plan 2 : Nonlinear localization

Localization analysis will be applied for geometric nonlinear model.

Macro scale result (/dscale,,1)

Micro scale result (/dscale,,1)

Application example (Homogenized solid rotating at large magnitude)

Localized

Material testing condition for localize are based on the strain matrix history of macro scale element.

2008 international ansys conference international ansys conference multiscale cae system for ... •...

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