IDENTIFICATION OF SWIFT LAW PARAMETERS USING FEMU BY A SYNTHETIC IMAGE DIC-BASED APPROACH

IDENTIFICATION OF SWIFT LAW PARAMETERS USING
FEMU BY A SYNTHETIC IMAGE DIC-BASED APPROACH
J. Henriquesa,*, M. Condea, A. Andrade-Camposa, J. Xavierb
*Corresponding author: joaodiogofh@ua.pt
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, 2829-516 Caparica, Portugal
25th International Conference on Material Forming
Braga, Portugal, 27-29 April 2022

2
J. Henriques, M. Conde, A. Andrade-Campos, J. Xavier - ESAFORM 2022 Conference, April 2022, Braga, Portugal
Outline
CAE Systems Manufacturing processes
Motivation and goals
1
Finite element model
updating technique
4
Material and numerical
model
2 Synthetic images and
digital image correlation
3
Results and discussion
5 Conclusions
6
Time steps
Measurement points
Optimization method:
- Levenberg-Marquardt algorithm.

Conclusions
6
5
Time steps
Measurement points
updating technique
4
3
model
3
Outline
1

4
1
- Reduced costs;
- Reduced time-waste;
- Increased quality.
Why?
▪ Computer-aided engineering systems play a key role in the simulation of
manufacturing processes.

5
1
▪ Given the recent advancements in image-based technology, there has been an
increase in the use of novel optical methodologies.
- Full-field measurements
coupled to inverse identification
methods and heterogeneous
testing.
- Reducing the number of
experimental tests required to
identify material parameters.

6
1
▪ The goal of this work is to identify the Swift hardening law parameters of the
DP600, using two approaches:
(i) Directly comparing the reference
with the FEA results;
(ii) Using DIC-levelled FEA data in the
comparison with the reference;

Conclusions
6
5
Time steps
Measurement points
updating technique
4
3
model
7
Outline
1

8
Material and numerical model
2
- The material used in this study is the DP600 steel;
- FEA under plane stress conditions using ABAQUS;
- Mesh is composed by 858 four-node plane stress
elements (CPS4R);
- The material behaviour is modelled using the
UMMDp[1].
[1] 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.

9
2
The constitutive model chosen assumes the following considerations:
▪ Isotropic linear elastic behaviour according to
Hooke’s Law;
▪ Isotropic hardening described by Swift law;
▪ Anisotropic behaviour described by Yld2000-2d
criterion[2].
[2] F. Barlat et. al. Plane stress yield function for aluminum alloy sheets—part 1: theory. International Journal of Plasticity,
19: 1297-1319, 2003.

[3] 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.
10
2
Hooke’s Law
E (GPa) ν
210 0.3
Yld2000-2d criterion
α1 α2 α3 α4 α5 α6 α7 α8 α
1.011 0.964 1.191 0.995 1.011 1.018 0.977 0.935 6
Swift Law
K [MPa] ε0 n
979.46 5.35×10-3 0.194
Reference parameters considered for the DP600 steel[3,4]:
[4] M. G. Oliveira, S. Thuillier, and A. Andrade-Campos.
Analysis of heterogeneous tests for sheet metal mechanical
behavior. Procedia Manufacturing, 47:831–838, 2020.

Conclusions
6
5
Time steps
Measurement points
updating technique
4
3
model
11
Outline
1

12
Synthetic images and digital image correlation
3
Reference image with FE mesh
Reference
synthetic image
Set of deformed
synthetic images

13
Synthetic images and digital image correlation
3
2D DIC settings
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

Conclusions
6
5
Time steps
Measurement points
updating technique
4
3
model
14
Outline
1

15
Finite element model updating technique
4
Time steps
Measurement points
• Levenberg-Marquardt algorithm.
K [MPa] ε0 n
Lower bound 500.00 1.00×10-6 1.00×10-6
Upper bound 1500.00 1.00×10-2 4.00×10-1

16
4
Generation of the reference virtual experimental strain fields and load data.

17
4
Direct comparison (FEA Methodology) Virtual experiment (VE Methodology)

Conclusions
6
5
Time steps
Measurement points
updating technique
4
3
model
18
Outline
1

19
5
K [MPa] ε0 n CF
FEA methodology
Run 2 – CPU time: 36 minutes (1.06 rel. time)
Identified parameters 968.83 3.80×10-3 1.87×10-1 1.57×10-4
Relative error [%] 1.09 28.48 3.81 -
VE methodology
Run 2 – CPU time: 287 minutes (8.44 rel. time)
Identified parameters 979.15 5.34×10-3 1.94×10-1 1.68×10-8
Relative error [%] 0.03 0.16 0.00 -

20
5

Conclusions
6
5
Time steps
Measurement points
updating technique
4
3
model
21
Outline
1

22
Conclusions
6
▪ This study compared the identification results for the swift hardening law by
using the traditional FEMU approach and by using a DIC-levelling approach.
▪ The results show a significant improvement in the identification accuracy
when using the DIC-levelled FEA data at the expense of increased
computational time.
▪ In future work, the VE methodology can be used to identify the constitutive
parameters of more complex constitutive models.

THANK YOU!
J. Henriquesa,*, M. Condea, A. Andrade-Camposa, J. Xavierb
* joaodiogofh@ua.pt
25th International Conference on Material Forming
Braga, Portugal, 27-29 April 2022
This project has received funding from the Research Fund for Coal and Steel under grant agreement No 888153.
The authors also gratefully acknowledge the financial support of the Portuguese Foundation for Science and
Technology (FCT) under the projects CENTRO-01-0145-FEDER-029713, POCI-01-0145 FEDER-031243 and
POCI-01-0145-FEDER-030592 by UE/FEDER through the programs CENTRO 2020 and COMPETE 2020, and
UIDB/00481/2020 and UIDP/00481/2020-FCT under CENTRO-01-0145-FEDER-022083. Authors also
acknowledge Fundação para a Ciência e a Tecnologia (FCT - MCTES) for its financial support via the projects
UIDB/00667/2020 (UNIDEMI). J. Henriques is also grateful to the FCT for the PhD grant 2021.05692.BD.
Acknowledgements

IDENTIFICATION OF SWIFT LAW PARAMETERS USING FEMU BY A SYNTHETIC IMAGE DIC-BASED APPROACH

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IDENTIFICATION OF SWIFT LAW PARAMETERS USING FEMU BY A SYNTHETIC IMAGE DIC-BASED APPROACH