2008 International ANSYS Conference International ANSYS Conference Multiscale CAE system for ... •...
Transcript of 2008 International ANSYS Conference International ANSYS Conference Multiscale CAE system for ... •...
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2008 International ANSYS Conference
Multiscale CAE system for wide field problems
Mr. Koji YamamotoApplication EngineerCYBERNET SYSTEMS CO.,LTD.
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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
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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
……………..
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• 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.
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• 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.
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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…)
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Function of Multiscale CAE System
• 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.
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Function of Multiscale CAE System
• 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
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Function of Multiscale CAE System
• 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
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Multiscale CAE System
• Multiscale CAE System GUI (ANSYS Classic)
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Multiscale CAE System
• Multiscale CAE System GUI( ANSYS Workbench)
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⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
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
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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
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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
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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
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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
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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
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Demonstration : Macro scale analysis
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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]
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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
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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
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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.