1) The document describes research to independently validate a method for designing generic specimen geometries that optimize identification of plastic anisotropy parameters through inverse modeling. 2) Specimen designs were optimized using an Indicator-IT criteria and shape optimization algorithm. The resulting designs were then validated via identifiability analysis and finite element model updating. 3) Preliminary results found that the optimized specimens had higher Indicator-IT values, better identifiability indices, and allowed for more accurate identification of anisotropic plasticity parameters compared to initial specimen designs.

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Independent Validation of Generic Specimen Design for Inverse Identification
of Plastic Anisotropy
Yi Zhanga , S. Coppietersa,*, S. Gothivarekara, A. Van de Veldea , D. Debruynea
a Department of Materials Engineering, KU Leuven, Technology Campus Ghent, 9000 Gent, Belgium
Belgium,19 March 2021
Presented by Yi Zhang
https://www.kuleuven.be/wieiswie/en/person/00127451

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I. Design optimal heterogeneous mechanical test based on Indicator- IT and shape optimization
algorithm.
II. Validate the optimization scheme via identifiability analysis and FEMU(Finite Element Model
Updating ).
III. Preliminary exploration of the identification quality assessed via identifiability analysis method.
Objectives of this Research Work

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• Sheet metal forming
• Modeling and simulation
Intro Problem Statement “Independent Validation of Generic Specimen
Design for Inverse Identification of Plastic Anisotropy”
High cost due to
try-and-error
manufacturing
Try-less manufacturing
Computer simulation
Die design
Accurate numerical
simulation
Material modelling
s Heterogeneous test
specimens
?
Complex
Model
Anisotropic
Behavior
Multiple
parameters
 Reduce mechanical tests
 Assessment of identifiability for specimen
 Accuracy parameters identification

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     
2 1
2 1 Max
1 2 3 4 5
1 2 3 4 5
Mean Std
Mean Std /
/
p p
R
r r r r r
a a a a a
Av p
w w w w w
w w w w w
T
I 

 
  
 
 
   
    
Strain state Strain level
Rank/Rate/Guide
Specimen
design[1]
Higher Indicator
Better specimen
Richer Strain
state
Richer Strain
Level
Wr Relative weighting factors Wa Absolute weighting factors
Formability Resistance to deformation
𝜺𝟐 𝜺𝟏 𝑹
Scatter
Standard deviation
(a)
(b)
(1)
Intro - Definition of an Indicator-IT
[1] N. Souto, Thuillier S, Andrade-Campos A. Design of an indicator to characterize and classify mechanical tests for sheet metals.
International Journal of Mechanical Sciences, 2015, 101-102, pp.252-271.

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Identifiability
Purpose:
• Identify unique parameters or improve identification accuracy.
Structural & Practical
• Equations vs Data
Non-identified and identified parameters subset:
• Model structure, parameters sensitivity(Geometry, material orientation, loading… )
Evaluate the identification quality potential before the FEMU.
Intro -Identifiability
comic by Olivia walch!(UM)
http://mogenquest.net
Example: Y=(m1+m2)X+b

6. TD
(b)
(a)
(c)
AOI
R4
30
L
ΔL
L=[0-9]
69
30
30
Fixed
t = 1.2
RD
Fixed edge
(U1,2,3=UR1,2,3=0)
Set:‘AOI’
3D-Shell (S4R)
Global seed: 2
Local seed: 0.3
Displacement, U2=δ
(U1,3=UR1,2,3=0)
𝛿
RD
TD
Symmetry
LA
LC
LD
LB
30o
.
.
. .
C
D
A
B
30o
30o
Spline
Fig. 1 FE model information with (a) specimen gemotry, (b) material orientations (c) mesh information and boundary conditions.
The research object
Model

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Table 1. Swift’s hardening law fitted in a strain range from εeq
pl = 0.002 up to the maximum uniform strain 𝜀𝑚𝑎𝑥. The reported R-values are measured at an engineering strain 𝜀𝑒𝑛𝑔 = 0.10[1]
The research object
Material properties
[1] Coppieters, S., Hakoyama, T., Eyckens, P. et al. On the synergy between physical and virtual sheet metal testing: calibration
of anisotropic yield functions using a microstructure-based plasticity model
0
50
100
150
200
250
300
350
400
0 0.05 0.1 0.15 0.2 0.25
True
stress
σ
(Mpa)
Logarithmic plastic strain εp
Swift's hardening law
𝝈 =K(εo+εp)𝒏
RD
45D
90D
Tensile direction σ0.2(MPa) K(MPa) ε0 n r εmax
RD 153 564 0.0059 0.275 1.85 0.248
45D 161 558 0.0072 0.272 1.93 0.254
TD 162 549 0.0080 0.272 2.82 0.259
Fig. 2 Uniaxial stress-strain curves at 0o, 45o and 90o with respect to rolling direction(RD).
Fig. 1(a) Orthotropic axes of the rolled sheet metals, (b) specimen orientation.

8. Optimization procedures
Fig. 1 Python Script structure for automatic numerical model, data post-processing and optimization

9. Table 1. IT value for different initial geometry parameters set and optimal geometry parameters.
Fig. 1 Geometry of mechanical tests (a) Test A, (b) Test B (c) Test C.
Optimization Results
* IT value at maximum uniform strain. Note: Anisotropic parameters change as a function of the plastic deformation[3]
[3] Coppieters S, Hakoyama T, Eyckens P, et al. On the synergy between physical and virtual sheet metal testing: calibration of anisotropic yield functions using a microstructure-based
plasticity model. International Journal of Material Forming, 2018, pp.741-759.
Test
Length vector L - [LA, LB, LC, LD] Post-Necking Equal Max 𝜀𝑒𝑞
𝑝𝑙
LA/mm LB/mm LC/mm LD/mm IT IT
Test A Initial 0.00 0.00 0.00 0.00 0.25 0.01*
Test B
Initial 2.80 2.80 2.80 2.80 0.23
Optimal 2.12 3.54 3.49 2.10 0.26 0.14
Test C
Initial 3.00 3.00 6.00 6.00 0.26
Optimal 2.87 4.81 7.23 7.23 0.34 0.15
 IT –Necking criterion/strain level
 IT value: Test A close to zero
 IT Rank: Test C>Test B>Test A

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Optimization Results- Stress states
(a) Test B (b)Test C
 Similar distribution shape
 Test C covers bigger area
Fig. 1 Stress states for Test B and Test C at TD material orientation using Hill1948 criterion

11. Fig. 1 Strain states for Test B and Test C.
(a) Test B and Test C
(b) Test B (c) Test C
1.14
1.43
0
0.4
0.8
1.2
1.6
Test B Test C
Strain state range
(1)
0.12
0.13
0.1
0.11
0.12
0.13
0.14
Test B Test C
Standard deviation of strain state
(2)
Optimization Results- Strain states
Fig.2 (1)-strain state range ((ε2/ε1)max-(ε2/ε1)min) , (2)-std(ε2/ε1) for Test B and Test C

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Fig. 1 IT value at certain load step of last increment of numerical simulation (a) and corresponding identifiability index using IK criterion (b) and 𝛾𝑘 criterion(c) for
three mechanical tests.
4.28
4.63
4.96
0 5 10 15 20 25
Test C
Test B
Test A
Collinearity index 𝛾K for three mechanical tests
1.48
1.60
1.68
0 1 2 3 4
Test C
Test B
Test A
Identifiability index IK for three mechanical tests
(b) (c)
Poor identifiability
(IK>3)
Moderate
(2<IK >3)
Good
(IK <2)
Poor identifiability
(𝛾𝐾 >20)
0.15
0.14
0.01
0 0.05 0.1 0.15 0.2
Test C
Test B
Test A
IT value at certain load step for three mechanical tests
(a)
Validation- Identifiability
Lower Indentifiability Index
Better Indentifiability
IT value:
Test C>Test B>Test A
validation
IK, 𝛾𝐾
value :
Test A>Test B>Test C
• Both of the specimens could be well identified.
• Identifiability exhibits good correlation with IT

13. Fig. 1 The detailed flowchart of FEMU procedure.
FEMU process

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F G H N
R.E.
Reference values 0.2302 0.3509 0.6492 1.4120
Identified
values
Test A 0.2274 0.3824 0.6176 1.3419 3.68%
Test B 0.2210 0.3658 0.6342 1.3679 3.13%
Test C 0.2192 0.3824 0.6340 1.3936 2.49%
Table 1. Comparison of correct parameters values and identified parameters values for Test A, Test B and Test C, respectively.
Fig. 1. Normalized identified yield loci compared with the reference yield locus. Test A (a), Test B (b) and Test C (c).
Validation- FEMU
Identified Accuracy:
Test C>Test B>Test A
IT value:
Test C>Test B>Test A
IK value 𝜸𝑲
:
Test A>Test B>Test C
IT , IK and 𝜸𝑲
show good
correlation with
Identified accuracy

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Limitations:
 IT -based design probably be enhanced by adjusting the weight factors and didn’t consider
material orientation.
 Identifiability analysis is only the numerical simulation, the high quality identification need sufficient
and accuracy experiment data.
Conclusions:
 Optimal mechanical test was obtained via IT and shape optimization method .
 IT value, identifiability index and identification accuracy show good correlation.
 Identifiability analysis could quantitatively predict the identification potential/quality
for anisotropic plastic constitutive parameters.
Limitations &Conclusions

16. Thank you for listening!