TechMA 2022 M. Conde (a), *, S. Coppieters (b), A. Andrade-Campos (a) (a) - Centre for Mechanical Technology and Automation (TEMA), Department of Mechanical Engineering, University of Aveiro; (b) - Department of Materials Engineering, KU Leuven(a) Aveiro, Portugal; (b) – Ghent, Belgium * – marianaconde@ua.pt

1. SUSTAINABLE MANUFACTURING SOLUTIONS
On the selection of constitutive models
for realistic numerical simulations
M. Conde (a), *, S. Coppieters (b), A. Andrade-Campos (a)
(a) - Centre for Mechanical Technology and Automation (TEMA), Department of Mechanical
Engineering, University of Aveiro; (b) - Department of Materials Engineering, KU Leuven
(a) Aveiro, Portugal; (b) – Ghent, Belgium
* – marianaconde@ua.pt

2. SUSTAINABLE MANUFACTURING SOLUTIONS
Virtualization and
realistic
simulations
• Adequate constitutive
model
• Accurately identified
parameters
Development and
manufacturing
• Precise results
• No delays
• No waste
Industries
• High quality
• Low costs
• High efficiency
Background of the topic
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3. SUSTAINABLE MANUFACTURING SOLUTIONS
Observed problem: constitutive models
Power laws
•Hollomon
•Swift
•Ludwick
Modified Power
Laws
•Voce
•Hockett and
Sherby
Flow rules
Isotropic hardening
Kinematic
hardening
•Linear
•Non-linear
Rotational
hardening
Distortional
hardening
Mixed hardening
Microstructural
models
Models for high
temperatures
Hardening laws
Isotropic
•Tresca
•Huber
•von Mises
•Hosford
•Cazacu and Barlat
•Drucker’s criterion
•Cazacu
•BC2000
•BBC2003
•BBC2005
•BBC2008
•Vegter criterion
Anisotropic
•Hill 48
•Hill 90
•Barlat 1989
•Barlat 2000
•Barlat 2004-18p
Yield functions
Forming limit
diagram (FLD)
Forming limit stress
diagram (FLSD)
Extended stress-
based limit curve
(XSFLC)
Polar diagram of
the effective plastic
strain (PEPS)
Fracture forming
limit diagram (FFLD)
Linear methods
•Swift
•Hill
•Storen and Rice
•Modified Mohr-
Coulom (MMC)
fracture criterion
Forming limits

4. SUSTAINABLE MANUFACTURING SOLUTIONS
Observed problem: constitutive models
More than 13000 possible
combinations of models

5. SUSTAINABLE MANUFACTURING SOLUTIONS
Observed problem: constitutive models
What model should I use for a
realistic simulation?
What strategy should I follow
to find the adequate model?

6. SUSTAINABLE MANUFACTURING SOLUTIONS
Observed problem: model selection
Direct comparison
Numerical and experimental data
Brute-force strategy
Model calibration
Several different models
Laboured task
Requires specialized knowledge
Time consuming task
Experimental data generation and
analysis
Non-precise selection strategy
Geometrical measurement, load
displacement curve or yield loci plot
Limited analysis
Model, material, mechanical phenomenon
and mechanical process
Ben-Elechi et al. 2021; Chatziioannou et al. 2021; Prakash et al. 2020; Kilic et al. 2018; Hou et al. 2017; Barros et al. 2016; Lin et al. 2020; Moreira
et al. 2014; Oliveira et al. 2007; Laurent et al. 2009; Nedoushan et al. 2014; Tuo et al. 2021.

7. SUSTAINABLE MANUFACTURING SOLUTIONS
Proposed solution: main goals
Automatic model selection
strategy
Pre-selection of model types
based on empirical knowledge
Definition of model types
priority list
Statistical and data analysis for
model selection and KPI’s

8. SUSTAINABLE MANUFACTURING SOLUTIONS
Proposed solution: empirical knowledge for pre-selection of models
Monotonous
processes
Isotropic
hardening
Changes in
strain path
Kinematic
hardening
Softening
over-
prediction
Non-linear
kinematic
hardening
Bruschi et al. 2014

9. SUSTAINABLE MANUFACTURING SOLUTIONS
Proposed solution: empirical knowledge for pre-selection of models
Isotropic
behaviour
von Mises
Properties
dependent on
the direction
Anisotropic
yield function
Hill48
model
Bruschi et al. 2014; Banabic et al. 2020

10. SUSTAINABLE MANUFACTURING SOLUTIONS
Proposed solution: model priority list definition
Deep-drawing test and
split-ring test
Aluminium alloy and steel
Yield function > Hardening rule
Accurate prediction of material’s behaviour
Prakash et al. 2020; Laurent et al. 2009

11. SUSTAINABLE MANUFACTURING SOLUTIONS
Proposed solution: model priority list definition
Hemispherical punch
stretching, deep drawing and
bending drawing tests
metals
Yield function > Kinematic hardening
Accurate prediction of material’s behaviour
Moreira et al. 2004

12. SUSTAINABLE MANUFACTURING SOLUTIONS
Proposed solution: conclusion
Realistic
simulations
KPI’s and
data
analysis
Automatic
model
selection

13. SUSTAINABLE MANUFACTURING SOLUTIONS
On the selection of constitutive models
for realistic numerical simulations
Acknowledgements: This project has received funding from the Research Fund for Coal and Steel under grant agreement No 888153. The authors also
acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT) under the project PTDC/EME-APL/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. Mariana
Conde is grateful to the Portuguese Foundation for Science and Technology (FCT) for the PhD grant 2021.06115.BD.
M. Conde (a), *, S. Coppieters (b), A. Andrade-Campos (a)
(a) - Centre for Mechanical Technology and Automation (TEMA), Department of Mechanical
Engineering, University of Aveiro; (b) - Department of Materials Engineering, KU Leuven
(a) Aveiro, Portugal; (b) – Ghent, Belgium
* – marianaconde@ua.pt

14. SUSTAINABLE MANUFACTURING SOLUTIONS