Sam Coppieters, A. Gil Andrade-Campos et al. MatchID Global User Meeting 2023 22 February2023 | Southampton, UK

1. On the power of virtual
experimentation in MT2.0:
a VFORM-xSteels outlook
Sam Coppieters, A. Gil Andrade-Campos et al.
MatchID Global User Meeting
On the power of virtual experimentation in MT2.0 : a
VFORM outlook
22 February2023 | Southampton, UK

2. Outline
• The vForm-xSteels project;
• The power of virtual experimentation in MT2.0
 Virtual experimentation (DVT)
 DVT vs. Actual Experiment
 CMAT: stress integration algorithms
• The power of virtual experimentation in ML approaches
 The methodology
 The case study of the Biaxial cruciform test
 The virtual experiments data-base
 Robustness analysis

3. Team Work: vForm-xSteels
Just some faces
but many more
are contributing!

4. VFORM-xSteels

5. Toward virtual forming and design:
Thermomechanical characterization of advanced
high strength steels through full-field
measurements and a single designed test
Call: RFCS-2019
Instrument: (RP / PDP / AM)
Start date: 01/06/2020
End date: 31/05/2024
Budget: €1,496,357.52
Type of Action: RFCS-RPJ
Number: 888153
Duration: 48 months
GA based on the: RFCS MGA — Multi - 2.null
Estimated Project Cost: €2,521,389.20
Requested EU Contribution: €1,496,357.52
This project has received funding from the Research Fund for Coal and Steel under grant agreement No 888153

6. Problem
Decades ago…

7. Problem
Today…

8. Problem and need
Increase information &
reduce time in material testing
Realistic simulations and material
behavior reproduction
Faster and accurate
development & production

9. Problem
Limited quality and amount of data
"The data we have is provided by suppliers. In some
cases it is limited."
André Ferreira
Designer Projectist @ OLI Oliveira e Irmãos
The new paradigm of
Material Testing 2.0
(previous seminar from F.
Pierron)

10. Problem
Error in material behavior virtual
predictions
"It would be important to have a service that could identify and
provide these data to companies in due time."
Mário Marques
Country Manager Iberia @ Autoform

11. Project goal
Nowadays, the use of numerical simulation in general and particularly finite element analysis (FEA) has
become a mandatory step (…) However, todays methods to characterize the materials through constitutive
models, including damage, and their parameters are expensive and not robust.
The main goal of the project VForm-XSteels is to develop an
efficient and accurate methodology for material characterization
and determining the material parameters of thermomechanical
models, from a dedicated single test that involve non-homogeneous
temperature and strain fields. Indeed, (…) A database and online library with calibrated
material constitutive models, particularly for AHSS, is also developed.
The benefits of the proposed methodology and consequent implemented numerical tool developed within
this project are (…) cost and time reduction in the overall development process are also benefits of this
proposal.

12. Project goal

13. Project goal and technology
IP test Optical
technology
Optimization
algorithms
Flexible
Accurate
Robust
Fast
Innovative ​experimental
test​ (1 000+ points)
Advanced Data analytics
to calibrate the material
models

14. WP3 - Design of a novel test using an integrated topology-shape
optimisation methodology and a thermo-mechanical indicator
• Mafalda Gonçalves, Thibault Barret, Antonio Andrade-Campos, Sandrine Thuillier
• Design by topology optimisation of a heterogeneous test to calibrate a viscoplastic model
• First from homogeneous tests (reference), then heterogenous tests Future work: thermal dependence to enhance the strain rate sensitivity
• KPI to quantify the
heterogeneity level: stress and
strain fields, stress triaxiality
and Lode parameter, rotation
angle, identifiability metrics,
DIC errors
• A heterogeneous test to
calibrate a viscoplastic model
• Synthetic images generated
with MatchID
• Investigation of the viscoplastic contribution
from hydraulic bulge test, DP600, thickness
0.8 mm
• Strain rate ranging from 10-3 up to 80 s-1
• Hydraulic bulge test, in quasi-static and
dynamic conditions (Hopkinson bars), strain
field measure using MatchID software
VISCOPLASTICITY HETEROGENEITY

15. Design of new heterogeneous specimens
Linear analysis; id = 0.0359 Nonlinear geometric
analysis; id = 0.0190
Nonlinear material and
geometric analysis; id = 0.0215
[6]
[7]

16. Thermomechanical heterogeneous test
Objective: developing a test with a combined
heterogenous temperature and strain field using a
Gleeble system
Multiphysics – coupled thermal-electrical-structural analysis
Select the best specimen and set-up

17. Thermomechanical heterogeneous test
Example of numerical results for one configuration
Temperature distribution
Plastic strain distribution
Testing zone

18. Status of UMAT structure in the VFM module and
integration with UMMDP/Fortran communication
D4.1 A large set of material user routines validated for commercial FEA software:
UMMDP has Fortran legacy (old Fortran)
Intermediate HUB

19. Status of Implementation of constitutive models in
UMAT routines
D4.1 A large set of material user routines validated for commercial FEA software
• Fully implemented for stress reconstruction
• Integrated within the Virtual Fields Module
• Youtube Tutorial XXXVII
• Stresses returned in global and material frame
• Fully parallelized
• Available in MatchID 2022.2
• Demo

20. Constitutive model: both plasticity and damage
behaviour depend on stress triaxiality and Lode angle!
Plasticity and damage behaviour

21. The power of virtual
experimentation (DVT) in MT2.0

22. FEDEF

23. Digital Virtual Twin (DVT)
Lava, P., Cooreman, S., Coppieters, S., De Strycker, M., Debruyne, D. (2009).
Assessment of measuring errors in DIC using deformation fields generated by plastic FEA.
Optics and lasers in engineering, 47 (7), 747-753.

24. Digital Virtual Twin (DVT)
FEMU platform
Calibrated material model

25. 3D plastic anisotropy though FEMU and DIC
Denys, K., Coppieters, S., Seefeldt, M., Debruyne, D. (2016). Multi-DIC setup for the identification of a 3D
anisotropic yield surface of thick high strength steel using a double perforated specimen. Mechanics of Materials,
100, 96-108.

26. DVT without FEDEF
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
0 2 4 6
Anisotropic
parameter
Iteration
N
M
L
ref
0.47
0.48
0.49
0.5
0.51
0.52
0.53
0.54
0 1 2 3 4 5 6
Anisotropic
parameter
Iteration
F
H
ref

27. DVT with FEDEF: two stereo DIC setups
Front data Side data

28. DVT with FEDEF: two stereo DIC setups
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
0 2 4 6
Anisotropic
parameter
Iteration
N
M
L
ref
0.47
0.48
0.49
0.5
0.51
0.52
0.53
0.54
0 1 2 3 4 5 6
Anisotropic
parameter
Iteration
F
H
ref

29. Actual experiments
Stereo 1: through-
thickness surface
Stereo 2: front
surface

30. Actual experiments: multi cam module

31. DVT vs. Actual Experiments
Virtual DIC data
2
C(θ)=
FEMU
Digital virtual
Twins
Initial Mesh
Load-
displacement
Numerical
simulations
Yld2000-2d (DH)
Real speckle pattern
Yld2000-2d
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
0 0.05 0.1 0.15 0.2 0.25 0.3
a1
a2
a3
a4
a5
a6
a7
a8
Prediction of what we will measure experimentally

32. DVT vs. Actual Experiments

33. Stress reconstruction (CMAT/AppStore)
IMPLICIT (SAMSTRESS)

34. Stress reconstruction (CMAT/AppStore)
EXPLICIT (MIRKOSTRESS)
Prof. M. Halilovič

35. The power of experimentation
in data-driven approaches
Numerical data meets real data through virtual experimentation

36. What’s the fuss about AI & data-driven approaches?
• Inverse methodologies for full-field measurements
Data-driven and Machine Learning methods
characterization by Dall-E

37. What’s the fuss about AI & data-driven approaches?
• Inverse methodologies for full-field measurements
Dall-E:
Full-field deformation measurement tools
designed for a complete engineering
analysis
MatchID global
user meeting
pencil drawing of
a finite element
analysis

38. • Builds the inverse problem model as non-linear
regressor (using data)
• Build the inverse model LLM and finds directly the
parameters solving A = LLM(εexp,Fexp).
• The inverse model LLM is boundary conditions’
dependent
• High computational cost for the creation of a suitable
samples’ database (direct problem database)
• A simulation software is required
Inverse methodologies for full-field measurements
General goal
for parameter identification
Data-driven and Machine Learning (ML) methods
The objective function can be written as
where

39. The objective function can be written as
Procedure for material parameter identification

40. Constitutive parameters Input Space
σ0 [MPa] 120-300
n 0.1-0.3
K [MPa] 280-700
R0 0.6-2.5
R45 0.6-2.5
R90 0.6-2.5
The case of the biaxial cruciform test
ML approach for the Cruciform test with swift’s hardening and Hill’s anisotropy
Cruciform tensile test
Total displacement ux=uy = 2 mm
405 CPS4R elements (reduced integration)
Anisotropic plastic behaviour (Hill 1948)
Latin Hypercube Sampling – 2000 simul.
R = 7 mm
30
mm
0x RD
0y TD
R = 2.5 mm
15 mm
ux = 2 mm
Symmetry boundary conditons
(uy = 0 mm)
Symmetry
boundary
conditons
(u
x
=
0
mm)
uy = 2 mm

41. Biaxial Cruciform test

42. XGBoost
Model
σ0
n
K
Strain xy
(20 time steps *
405 features per time step)
Strain yy
(20 time steps *
405 features per time step)
Strain xx
(20 time steps *
405 features per time step)
Total force 0x
(20 time steps *
1 feature per time step)
Total force 0y
(20 time steps *
1 feature per time step)
R0
R45
R90
24340 features 6 Outputs
In/out features definition for the ML inverse model
However…

43. Features importance analysis: SHAP
• Results
• ML approach - Cruciform test
σ0
n K

44. Features importance analysis: SHAP
46
R0 R45 R90

45. XGBoost
Model
σ0
n
K
Strain xy
(20 time steps *
114 features per time step)
Strain yy
(20 time steps *
114 features per time step)
Strain xx
(20 time steps *
114 features per time step)
Total force 0x
(20 time steps *
1 feature per time step)
Total force 0y
(20 time steps *
1 feature per time step)
R0
R45
R90
6280 features 6 Outputs
In/out features definition for the ML inverse model
Becoming …

46. Testing result
50
σ0 n K
R0 R45 R90
Test – 200 samples
2000 samples were generated, 1800 for training and 200 for testing

47. DIC levelling: the power of digital virtual testing (DVT)

48. DIC levelling: the power of DVT
Comparison of the displacement
magnitude in the cruciform test,
between FEA (left) and virtual
experiments (right).

49. Digital virtual tests (DVT) database
ML database for training
ML architecture
Synthetic
image
generator
FEA program
(e.g. Abaqus)
?
?
?
?
?
Each sample was divided into 6455 subsets. In each subset, the location in
pixels and the strains εxx, εyy, and εxy were recorded.
2000 samples were generated, 1800 for training and 200 for testing.

50. Synthetic
image
generator
FEA program
(e.g. Abaqus)
?
?
?
?
?
Digital virtual tests (DVT) database

51. … resulting in more than
400k features for each
sample.
To validate the models,
2000 images were
generated (1800 for training
and 200 for test).
only the regions of interest found with the SHAP values
were used to train the models (just 10% of the data)
number of
features was too
large
impossible to train
the model with
every feature
Digital virtual tests (DVT) database

52. Performance evaluation
σ0 n K
R0 R45 R90
Predictive
Simulated
R2=0.9980 R2=0.9610
R2=0.9779
R2=0.9779
R2=0.9923 R2=0.9925
Predicted (vertical axis) vs. real (horizontal axis) values of the constitutive
parameters
2000 samples were generated, 1800 for training and 200 for testing

53. DVT database results
• Results: virtual experiments database
• ML approach - Cruciform test
R2 and MAE for Abaqus vs MatchID database
The results are
still robust
even with DIC
noise/errors!

54. Robustness Analysis: material rotation
0
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25 30 35 40 45
Relative
error
(%)
Rotation ( )
Y0
K
n
r0
r45
r90
Relative error in the
prediction of the
material parameters as
a function of the
rotation of the material
axes w.r.t. the global
axes system.
In this context, one of the samples
from the testing set was chosen
(Y0=172 MPa, n=0.16; K=486 MPa;
r0=2.38; r45=1.8; r90=1.06) and the
orientation of the material axes was
varied w.r.t. the global axes system
0xy
P.A. Prates, J. Henriques, J. Pinto, N. Bastos and A. Andrade-Campos, Coupling machine learning
and synthetic image DIC-based techniques for the calibration of elastoplastic constitutive
models, Esaform conference 2023

55. On the power of virtual
experimentation in MT2.0:
a VFORM-xSteels outlook
Sam Coppieters, A. Gil Andrade-Campos et al.
MatchID Global User Meeting
On the power of virtual experimentation in MT2.0 : a
VFORM outlook
22 February2023 | Southampton, UK