ESAFORM 2022 M. Conde1, J. Henriques1, S. Coppieters2, A. Andrade-Campos1 1 TEMA, Department of Mechanical Engineering, University of Aveiro, Portugal 2 Department of Materials Engineering, Ghent Technology Campus, KU Leuven, Belgium

1. Parameter Identification of Swift law
using a FEMU-based approach and an
innovative heterogeneous mechanical
test
M. Conde1, J. Henriques1,
S. Coppieters2, A. Andrade-Campos1
1 TEMA, Department of Mechanical
Engineering, University of Aveiro, Portugal
2 Department of Materials Engineering, Ghent
Technology Campus, KU Leuven, Belgium
https://unsplash.com/photos/r4gqCg1iies

2. M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
1 Introduction, Framework and Literature Review
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
1
Realistic
simulations
Adequate
constitutive model
Accurate material
parameters
Material model calibration strategy

3. M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
1 Introduction, Framework and Literature Review
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
1
Material model
calibration
strategy
Classical
approach
Inverse
identification
approach
Non-
homogeneous
mechanical test
FFM
Several
mechanical tests
Simple strain and
stress fields

4. M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
1 Introduction, Framework and Literature Review
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
1
FEMU
Experimental data
(DIC)
Numerical data
(FEA)
Errors due to different measurement
techniques [1]
[1] P. Lava, E. M. C. Jones, L. Wittevrongel, and F.
Pierron, “Validation of finite-elemento models using
full-field experimental data : Levelling finite-element
analysis data through a digital image correlation

5. M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
1 Introduction, Framework and Literature Review
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
1
Proposed solution
Experimental data
(DIC)
Numerical data
(FEA-DIC) [2]
Same filtering, spatial resolution and strain
calculation method [1]
Optimised
heterogeneous
test
Dogbone test
[1] P. Lava, E. M. C. Jones, L. Wittevrongel, and F. Pierron, “Validation of finite-elemento models using
full-field experimental data : Levelling finite-element analysis data through a digital image correlation
engine,” Strain, vol. 56, no. e12350, 2020.
[2] J. Henriques, João;Conde, Mariana; Andrade-Campos, António; Xavier, “Identification of Swift law parameters using FEMU
by a synthetic image approach based on digital image correlation,” in Esaform 2022 - 25th International Conference on
Material Forming, 2022.

6. 2 Methodology and Implementation
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
2
Run virtual test in Abaqus
up to rupture
Nodal coordinates and
displacement of each step
Create synthetically
deformed images using
MatchID
Calculate FEMU cost
function value
Strain fields of each step
Convergenc
e
Best set of parameters
Create virtual test model
Run virtual test in Abaqus
up to rupture
Nodal coordinates and
displacement of each step
Create synthetically
deformed images using
MatchID
Strain fields of each step
Optimisation algorithm
New set of parameters
Reference set of
parameters
Initial set of parameters

7. 2.1 Mechanical Tests
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
3
P1 P2 P3 P4 P5 P6
xx
[mm]
0.000 3.708 23.092 23.505 15.889 3.086
yy
[mm]
10.000 11.421 31.784 17.078 5.163 0.000
Optimised heterogeneous test [3] Dogbone test
[3] M. Conde, A. Andrade-Campos, M. G. Oliveira, and
J. M. P. Martins, “Design of heterogeneous interior
notched specimens for material mechanical
characterization,” in Esaform 2021 - 24th

8. 2.1 Mechanical Tests
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
3
Optimised heterogeneous test [3] Dogbone test
[3] M. Conde, A. Andrade-Campos, M. G. Oliveira, and
J. M. P. Martins, “Design of heterogeneous interior
notched specimens for material mechanical
characterization,” in Esaform 2021 - 24th
P1 P2 P3 P4 P5 P6
xx
[mm]
0.000 3.708 23.092 23.505 15.889 3.086
yy
[mm]
10.000 11.421 31.784 17.078 5.163 0.000

9. 2.2 Constitutive Model and Material Definition
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
4
Hooke’s Law E [GPa] ν
210 0.3
Swift Law K [MP] 𝜀0 n
979.460 0.00535 0.194
Yld 2000-2d α1 α2 α3 α4 α5 α6 α7 α8 n
1.011 0.964 1.191 0.995 1.010 1.018 0.977 0.935 6
DP600 steel (0.8 mm thickness)
• Elastic behaviour: Hooke’s Law
• Hardening behaviour: Swift Law
• Anisotropy behaviour: Yld2000-2d function
• Damage initiation: Forming limit diagram criterion (FLDC)
[4] 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 Eng., vol. 81, no.
October, pp. 760–765, 2014 .
[4
]

10. 2.3 Analysis of the Test
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
5
• Plane stress state conditions
• Dogbone: 858 elements;
Heterogeneous: 2975 elements
• CPS4R element type
• Material behaviour: UMMDp [5]
• 10 evenly spaced time
increments
FEA (Abaqus) DIC (MatchID)
• Average speckle size: 3 px
• Subset size: 21 px
• Step size: 5 px
• Strain window size: 11 datapoints
• Subset shape function: quadratic
• Matching criterion: ZNSSD
• Interpolation: Bi-cubic spline
• Displacement noise-floor: 0.009 px
Initial mesh
Displacement
fields
[5] 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,” J. Phys.

11. 2.4 FEMU-Based Approach
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
7
Φ(χ) =
1
𝑛t
𝑖=1
𝑛t 1
3𝑛p 𝑗=1
𝑛p 𝜀𝑥𝑥
num(χ)−𝜀𝑥𝑥
exp
𝜀max
exp
2
+
𝜀𝑦𝑦
num(χ)−𝜀𝑦𝑦
exp
𝜀max
exp
2
+
𝜀𝑥𝑦
num(χ)−𝜀𝑥𝑦
exp
𝜀max
exp
2
𝑗
+
Fnum
(χ)−Fexp
Fmax
exp
2
𝑖
Minimization of:
In order to find:
χ =[𝐾, 𝜀0, ν]
Optimisation algorithm: Levenberg-Marquardt [6]
[6] S. Community, “Optimization - scipy.optimize,” SciPy.org, 2021. [Online]. Available:
https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html. [Accessed: 01-Oct-2021] .

12. 3 Analysis and Results
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
8
K 𝜀0 n Φ(χ)
Dogbone test
Ref. set 979.46 0.00535 0.194 1.055x10-9
Init. set 1 1000.0 0.00480 0.100 7.009x10-2
Final set 942.96 9.99x10-7 0.169 2.689x10-4
Error [%] 3.7265 100 12.9 -
Init. set 2 708.51 0.000573 0.218 8.830x10-2
Final set 979.14 0.00534 0.194 1.680x10-8
Error [%] 0.032671 0.187 0.000 -
Heterogeneous test
Ref. set 979.46 0.00535 0.194 2.665x10-8
Init. set 1 1000.0 0.00480 0.100 8.853x10-2
Final set 902.99 0.00457 0.103 5.153x10-2
Error [%] 7.8069 14.6 46.9 -
Init. set 2 708.51 0.000573 0.218 8.612x10-2
Final set 979.00 0.00533 0.194 3.323x10-8
Error [%] 0.046964 0.374 0.000 -

13. 3 Analysis and Results
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
8

14. 3 Analysis and Results
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
9

15. 4 Main Conclusions
M. Conde, J. Henriques, S. Coppieters, A. Andrade-Campos - Parameter identification of Swift law using a FEMU-based approach and an innovative heterogenous mechanical test
ESAFORM 2022 – 25th International Conference on Material Forming – Braga, Portugal
10
• Identification of the Swift’s hardening law parameters using a DIC-levelled
FEMU methodology
• Comparison of the identified parameters using an optimised strain
heterogeneous test and a dogbone test
• The optimisation process is very dependent of the initial set of parameters
• Parameters’ relative errors below 0.4% for both tests
• The optimised heterogeneous test lead to a more robust calibration
compared to the dogbone test
• The different strain states that the optimised specimen presents were not

16. Parameter Identification of Swift law
using a FEMU-based approach and an
innovative heterogeneous mechanical
test M. Conde, J. Henriques,
S. Coppieters, A. Andrade-Campos
marianaconde@ua.pt
Thank you for your
attention!
Acknowledgments
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. Mariana Conde is grateful to the Portuguese
Foundation for Science and Technology (FCT) for the PhD grant 2021.06115.BD
https://unsplash.com/photos/r4gqCg1iies