ESAFORM 2023 João Henriquesa,*, A. Andrade-Camposa , J. Xavierb aTEMA, Department of Mechanical Engineering, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal bUNIDEMI, Department of Mechanical and Industrial Engineering, NOVA School of Science and Technology, NOVA University Lisbon, 2825-149 Lisbon, Portugal

1. International ESAFORM Conference
Krakow, Poland, 19-21 April 2023
On the inverse identification of
sheet metal mechanical behaviour
using a heterogeneous Arcan virtual
experiment
João Henriquesa,*, A. Andrade-Camposa, J. Xavierb
aTEMA, Department of Mechanical Engineering, University of Aveiro, Campus
Universitário de Santiago, 3810-193 Aveiro, Portugal
bUNIDEMI, Department of Mechanical and Industrial Engineering, NOVA School of
Science and Technology, NOVA University Lisbon, 2825-149 Lisbon, Portugal
*Corresponding author: joaodiogofh@ua.pt

2. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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Outline
1
5
2
3
Framework
Material and numerical model
Heterogeneous test evaluation
Results and discussion
6 Closing remarks
4 DIC and inverse identification

3. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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1. Framework
Numerical simulation on sheet metal forming
• Accurate numerical results is highly dependent
on the constitutive model used and the
calibration of its parameters.
CAE Systems Manufacturing processes
Costs and time-waste
Why?
• Numerical simulation tools
are used in a wide range of
manufacturing processes.
Material-waste Sustainability in sheet metal part manufacturing
Product quality

4. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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1. Framework
Mechanical testing for material model calibration
[1] Vegter, H. & An, Y.G.. (2008). Mechanical testing for
modeling of the material behaviour in forming simulations.
Proceedings of the 7th International Conference and Workshop
on Numerical Simulation of 3D Sheet Metal Forming Processes,
Interlaken, Switzerland. 55-60.
MatchID, Metrology beyond colors.
• Classical mechanical tests leads to
poor kinematic data.
• Material testing 2.0[1]:
Heterogeneous tests, full-field
measurements coupled to
inverse identification.
[2] Pierron F, Grédiac M. Towards Material Testing 2.0. A review of test design for identification of
constitutive parameters from full-field measurements. Strain 2021.

5. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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1. Framework
Main goal
This work aims to do a numerical
investigation of heterogeneous states of
strainstress with the Arcan test
configuration:
• Variation in the load and rolling direction
angles: 0º, 45º and 90º.
• Use of heterogeneity criterions to select one
single configuration.
• Generate synthetically deformed speckle
pattern images and use the Virtual Fields
method to identify the material consitutitve
parameters
[2] A. Kumar, M.K. Singha, V. Tiwari. Structural response of metal sheets
under combined shear and tension. Structures, 26: 915-933, 2020.

6. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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2. Material and numerical model
• DP600 dual-phase steel with 0.8 mm
thickness.
• Numerical simulation under plane stress and
quasi-static conditions on ABAQUS.
• Mesh is composed by 2596 four-node plane
stress elements (CPS4R);
• The material behaviour is modelled using the
UMMDp[2].
[3] H. Takizawa, T. Kuwabara, K. Oide, and J. Yoshida. Development of the subroutine library ‘UMMDp’ for anisotropic yield functions commonly
applicable to commercial FEM codes. Journal of Physics: Conference Series, 734:032028, 2016.

7. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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2. Material and numerical model
• Isotropic linear elastic behaviour
according to Hooke’s Law;
• Isotropic hardening described by Swift
law;
• Anisotropic yielding described
by Hill48 criterion[3].
Constitutive models
[4] R. Hill. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. Lond. A, 193 281-297, 1948.
Hooke’s Law
E (GPa) ν
210 0.3
Hill48 criterion
F G H N
0.3748 0.5291 0.4709 1.1125
Swift Law
K [MPa] ε0 n
979.46 5.35×10-3 0.194 [5] F. Ozturk, S. Toros, and S. Kilic. Effects of anisotropic yield functions on prediction of forming limit
diagrams of dp600 advanced high strength steel. Procedia Engineering, 81:760–765, 2014.
G+H=1 condition for the Hill48
criterion is used

8. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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3. Test evaluation
Heterogeneity criterion: IT1
[6] N. Souto, S. Thuillier, A. Andrade-Campos. Design of an indicator to characterize and classify mechanical tests for sheet metals. Int. J. Mech. Sci., 101-102: 252-271, 2015.
wa1 wa2 wa3 wa4 wa5 wr1 wr2 wr3 wr4 wr5
1 4 0.25 1 1 0.3 0.03 0.17 0.4 0.1
Relative weights
Relative weights
Eq. plastic
strain
Major principal strain
Minor principal strain
Relative and absolute weights used [5].

9. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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3. Test evaluation
Heterogeneity criterion: rotation angle
[7 ] M. Guimarães Oliveira, S. Thuillier, A. Andrade-Campos. Analysis of Heterogeneous Tests for Sheet Metal Mechanical Behavior. Procedia Manuf., 47: 831-838, 2020.
Principal angle
Minor principal stress
Major principal stress
Stress components in the
material coordinate system

10. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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4. DIC and inverse identification
Synthetic image generation and digital image correlation
2D DIC settings - MatchID software
Correlation criterion: ZNSSD
Interpolation: Bicubic spline
Shape function: Quadratic
Subset size: 21 px
Step Size: 5 px
Image pre-filtering: Gaussian, 5 px kernel
Strain window size: 11
Strain interpolation: Bilinear Q4
Strain convention: Green-Lagrange
Displacement noise-floor: 0.009 px
Strain noise-floor: 1.246×10-4
Hardware settings
Camera: Flir Blackfly BFS-U3-51S5M-C
Focal length: 12.5 mm
Image resolution: 2448×2048 px2
Camera noise: 0.48% of range
Working distance: 251 mm
Image conversion factor: 0.05039 mm/px
Speckle pattern: Numerically generated
Average speckle size: 3 px

11. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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4. DIC and inverse identification
Virtual fields method
• The Virtual Fields Method (VFM) is widely used for material identification.
• Based on the principle of virtual work:
Internal work External work
[8] M. Grédiac, F. Pierron, S. Avril, and E. Toussaint. The Virtual Fields Method for Extracting Constitutive Parameters From Full-Field Measurements: a Review. Strain, vol. 42, no. 4. Wiley, pp. 233–253, 2008.
Virtual displacements
External force
Cauchy stress tensor
Virtual strains
• The VFM module from MatchID software is used for the identification.

12. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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5. Results and discussion
Heterogeneity criterion: IT1
α: Loading direction (0º is tensile test)
ϴ: Rolling direction

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α: 0º
ϴ: 45º
α: 45º
ϴ: 90º
α: 90º
ϴ: 90º

14. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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5. Results and discussion
Comparison of principal strains

15. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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5. Results and discussion
Identification results – VFM
F G H N K [MPa] ε0 n
Best identification run (run 3) – Final residual = 0.4432
Identified parameters 0.487 0.670 0.330 1.428 1086.00 3.71×10-3 0.188
Relative error [%] 29.99 26.71 30.01 28.36 10.88 30.65 3.35

16. On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
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5. Results and discussion
Identification results Yield surface – comparison between reference
and identified parameters (best id. run)

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On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
Closing remarks
• The IT1 criterion proved to be a good quantitative evaluation of the
heterogeneity of the material's strain field, which appears to have a
significant influence on the inverse dentification of the hardening
parameters.
• The rotation angle parameter is a better criterion for assessing the
anisotropy sensitivity of mechanical tests.
• While the Arcan test setup provides interesting combinations of
stressstrain states it was not possible to identify all constitutive
parameters with a single test. Moreover, the uncertainty propagation
throughout the identification process also has an impact on the identified
parameters, resulting in deviations from the ground-truth parameters.

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On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, J. Henriques et al., 2023
Closing remarks
Future work
• Other test configurations could be used for the inverse identification of the
isotropic hardening and anisotropic yielding parameters by finding a good
balance between the IT1 and the rotation angle criterions.
• Additionally, a greater number of uniform virtual fields could be used in the
inverse identification of the constitutive parameters, as could automatic
virtual field selection strategies such as sensitivity-based virtual fields.
• An experimental campaign with the Arcan test is also planned as future
work. Moreover, in the future multiple test configurations can also be used
in the identification procedure to increase the accuracy of the parameter
identification.

19. On the inverse identification methods for forming plasticity models using full-field measurements, A. Andrade-Campos et al., IDDRG2022, France
Thank you for your attention!
International ESAFORM Conference
Krakow, Poland, 19-21 April 2023
João Henriques*, A. Andrade-Campos, J. Xavier
*Corresponding author: joaodiogofh@ua.pt
Acknowledgements
J. Henriques is grateful to the Portuguese Foundation for Science and Technology (FCT) for the Ph.D. grant 2021.05692.BD. This project has
received funding from the Research Fund for Coal and Steel under grant agreement No 888153. The authors gratefully acknowledge the
financial support of the FCT under the project PTDC/EMEAPL/29713/2017 by UE/FEDER through the programs CENTRO 2020 and COMPETE
2020, and UID/EMS/ 00481/2013-FCT under CENTRO-01–0145-FEDER-022083. The authors also acknowledge the FCT (FCT - MCTES) for its
financial support via the projects UIDB/00667/2020 (UNIDEMI).
Any questions?