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Federated Learning of Neural Network Models with Heterogeneous Structures.pdfKundjanasith Thonglek
Federated learning trains a model on a centralized server using datasets distributed over a large number of edge devices. Applying federated learning ensures data privacy because it does not transfer local data from edge devices to the server. Existing federated learning algorithms assume that all deployed models share the same structure. However, it is often infeasible to distribute the same model to every edge device because of hardware limitations such as computing performance and storage space. This paper proposes a novel federated learning algorithm to aggregate information from multiple heterogeneous models. The proposed method uses weighted average ensemble to combine the outputs from each model. The weight for the ensemble is optimized using black box optimization methods. We evaluated the proposed method using diverse models and datasets and found that it can achieve comparable performance to conventional training using centralized datasets. Furthermore, we compared six different optimization methods to tune the weights for the weighted average ensemble and found that tree parzen estimator achieves the highest accuracy among the alternatives.
Presentation by Dr Steffi Friedrichs, entitled: Nanotechnology at the Crossroads of Converging Technologies: Unveiling the Future of Innovation
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Doctoral Programme in Mechanical Engineering
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Parameter Identification of Swift law using a FEMU-based approach and an inno...vformxsteels
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2 Department of Materials Engineering, Ghent Technology Campus, KU Leuven, Belgium
Parameter Identification of Swift law using a FEMU-based approach and an inno...vformxsteels
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2 Department of Materials Engineering, Ghent Technology Campus, KU Leuven, Belgium
Federated Learning of Neural Network Models with Heterogeneous Structures.pdfKundjanasith Thonglek
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Design and validation of a heterogeneous interior notched specimen for materi...Vform Xsteels
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6th International Conference on Mechanical Engineering (MEN 2023)ijccmsjournal
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On the selection of constitutive models for realistic numerical simulationsvformxsteels
TechMA 2022
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* – marianaconde@ua.pt
On the selection of constitutive models for realistic numerical simulationsvformxsteels
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(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
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3810-193 Aveiro, Portugal
bUNIDEMI, Department of Mechanical and Industrial Engineering, NOVA School of Science and Technology,
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IDENTIFICATION OF SWIFT LAW PARAMETERS USING FEMU BY A SYNTHETIC IMAGE DIC-BA...vformxsteels
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, J. Xavierb
*Corresponding author: joaodiogofh@ua.pt
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3810-193 Aveiro, Portugal
bUNIDEMI, Department of Mechanical and Industrial Engineering, NOVA School of Science and Technology,
NOVA University Lisbon, 2829-516 Caparica, Portugal
5th International Conference on Trends in Mechanical Engineering (MECE 2021)meijjournal
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RS2022
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6th International Conference on Materials Science and Engineering (MSE 2022)msejjournal
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6th International Conference of Advances in Materials Science and Engineering...ijccmsjournal
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International Conference on Computational Science & Applications (COMSAP 2023)ijdpsjournal
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* marianaconde@ua.pt
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2 Department of Materials Engineering, Ghent Technology Campus, KU Leuven, Belgium
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2 Department of Mechanical Engineering, University of Aveiro, 3810-193
Aveiro, Portugal
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M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Virtualization of processes
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
Images source: https://unsplash.com/photos/jHZ70nRk7Ns ; https://unsplash.com/photos/SVUqHTVyn6w ; https://unsplash.com/photos/t9DooibgMEk
3. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Virtualization of processes
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
Images source: https://unsplash.com/photos/jHZ70nRk7Ns ; https://unsplash.com/photos/SVUqHTVyn6w ; https://unsplash.com/photos/t9DooibgMEk
4. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Virtualization of processes
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
Images source: https://unsplash.com/photos/jHZ70nRk7Ns ; https://unsplash.com/photos/SVUqHTVyn6w ; https://unsplash.com/photos/t9DooibgMEk
5. Isotropic
hardening
laws
Yield
functions
International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
Kinematic
hardening
laws
Damage
models
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Material constitutive models in the literature
6. Isotropic
hardening
laws
Yield
functions
International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
Kinematic
hardening
laws
Damage
models
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Material constitutive models in the literature
7. Isotropic
hardening
laws
Yield
functions
International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
Kinematic
hardening
laws
Damage
models
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Material constitutive models in the literature
12. Isotropic
hardening
laws
Yield
functions
International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
Kinematic
hardening
laws
Damage
models
Introduction and framework
Material constitutive models in the literature
More than 1300possible
combinations of models
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
13. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Material constitutive models selection in the literature
Brute-force
Direct comparison
Numerical and experimental data
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.
14. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Introduction and framework
Material constitutive models selection in the literature
Automatic
selection tool
Direct comparison
Numerical and experimental data
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.
15. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Application of the proposed solution
Unknown numerical material behaviour
How to model the material
behavior?
What constitutive models?
What material parameters?
16. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Application of the proposed solution
Unknown numerical material behaviour
• DP600 dual-phase steel
• AA3104 aluminium alloy
• Material parameters from literature
17. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Application of the proposed solution
Constitutive models and materials
DP600
Elastic
properties
E [Gpa] ν
210.000 0.300
Swift law K [Mpa] 𝜀0 n
979.460 0.00535 0.194
Voce law 𝜎y0 Q b
815.600 407.922 7.869
Yld2000-2d
criterion
𝛼1 𝛼2 𝛼3 𝛼4 𝛼5 𝛼6 𝛼7 𝛼8
a
1.011 0.964 1.191 0.995 1.010 1.018 0.977 0.935 6.00
A-F model C [Mpa] 𝛾
28896.000 121.000
18. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Application of the proposed solution
Constitutive models and materials
AA3104
Elastic
properties
E [Gpa] ν
68.950 0.330
Swift law K [Mpa] 𝜀0 n
363.128 0.000229 0.0275
Voce law 𝜎y0 Q b
351.260 62.400 27.205
Yld2000-2d
criterion
𝛼1 𝛼2 𝛼3 𝛼4 𝛼5 𝛼6 𝛼7 𝛼8
a
0.594 1.177 0.818 0.892 0.967 0.627 0.947 1.152 8.00
A-F model C [Mpa] 𝛾
22885.000 400.000
19. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Application of the proposed solution
Unknown numerical material behaviour
How to get more accuracy in
simulations?
What constitutive models
should I use to improve the
calibration?
Is kinematic hardening
relevant? Or anisotropy?
20. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
21. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
22. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
23. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
24. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
25. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
26. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
27. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
28. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Proposed solution
Process-informed material model selection
Sheet metal forming
simulation
Selected
constitutive
models
Material
parameters
Simulation
specifications
Measurements
of interest/critical
for the process
ANOVA analysis
Constitute models
importance ranking
Mechanical
process
configuration
Constitutive models (UMMDp)
29. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
Mechanical process configuration
Hole expansion test configuration
Blank with 0.8 mm thickness
R12
R12
55
50
Punch
Die
35
150
30. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
Simulation specifications
Abaqus/Standard software
Blank: 3D deformable shell
revolution
Tools: 3D analytical rigid shell
revolution
R12
R12
55
50
Punch
Die
31. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
Simulation specifications
Step-1:
Punch with displacement
condition
Blank fixed in outer edge
Die fixed
Punch
Die
32. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
Simulation specifications
Step-1:
Punch with displacement
condition
Blank fixed in outer edge
Die fixed
Punch
Die
33. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
Simulation specifications
Step-2:
Tools release
Springback observation
Punch
Die
34. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
Simulation specifications
Structured mesh
6400 elements
9 integration points along
thickness
S4R (4-node shell) elements
with reduced integration
35. Type of
constitutive
model
Forming
simulation
observable
International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
ANOVA approach
ANOVA
Independent variables (groups):
Isotropic hardening law
Yield criterion
Kinematic hardening law
Dependent variables:
Hole’s circularity
Maximum punch force
Springback factor
36. Type of
constitutive
model
Forming
simulation
observable
International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
ANOVA approach
ANOVA
The null hypothesis is that there is no difference among the groups’ means
The alternative hypothesis is that the averages are not all equal
If any group means is significantly different from the overall mean, the null
hypothesis is rejected. This is observed with the p-value
37. Type of
constitutive
model
Forming
simulation
observable
International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
ANOVA approach
ANOVA
The p-value is the probability of obtaining the observed results, assuming that
the null hypothesis is true
A p-value lower than 0.05 considers the statistical meaning of the analysed
group
The smaller the p-value is, the more significant is the result
38. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Implementation
3-way ANOVA analysis
Run Isotropic hardening law Yield function Kinematic hardening law
1 Voce’s law von Mises Not considered
2 Voce’s law von Mises A-F model
3 Voce’s law Yld2000-2D Not considered
4 Voce’s law Yld2000-2D A-F model
5 Swift’s law von Mises Not considered
6 Swift’s law von Mises A-F model
7 Swift’s law Yld2000-2D Not considered
8 Swift’s law Yld2000-2D A-F model
39. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Results
Simulations’ output Run 1 2 3 4 5 6 7 8
IHL V V V V S S S S
YF vM vM Y2000 Y2000 vM vM Y2000 Y2000
KHL None A-F None A-F None A-F None A-F
40. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
Factors Hole’s
circularity p-
value
Maximum
punch force p-
value
Springback
factor p-value
p-value
average
Ranking
DP600
Isotropic hardening law 7.131E-1 1.078E-8 2.534E-7 2.377E-1 2
Yield function 2.342E-4 1.436E-2 9.715E-1 3.287E-1 3
Kinematic hardening law 1.282E-1 8.716E-8 1.444E-6 4.274E-2 1
AA3104
Isotropic hardening law 2.020E-1 3.099E-4 9.909E-6 6.743E-2 2
Yield function 6.778E-4 8.624E-2 1.037E-5 2.898E-2 1
Kinematic hardening law 4.913E-1 2.881E-4 1.569E-5 1.639E-1 3
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Results
ANOVA analysis
41. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Results
DP600 Strain path changes
44 39
35
18
42. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Results
AA3104 Strain path changes
44 39
35
18
43. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
Factors Hole’s
circularity p-
value
Maximum
punch force p-
value
Springback
factor p-value
p-value
average
Ranking
DP600
Isotropic hardening law 7.131E-1 1.078E-8 2.534E-7 2.377E-1 2
Yield function 2.342E-4 1.436E-2 9.715E-1 3.287E-1 3
Kinematic hardening law 1.282E-1 8.716E-8 1.444E-6 4.274E-2 1
AA3104
Isotropic hardening law 2.020E-1 3.099E-4 9.909E-6 6.743E-2 2
Yield function 6.778E-4 8.624E-2 1.037E-5 2.898E-2 1
Kinematic hardening law 4.913E-1 2.881E-4 1.569E-5 1.639E-1 3
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Results
ANOVA analysis
44. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Results
Materials anisotropic behaviour
45. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
• A process-informed material constitutive model comparison
and selection strategy was proposed
• ANOVA was used to find a relation between the constitutive
models and the measurements of interest in a forming
simulation
• A model’s importance ranking was established based on the p-
values
• This information can conduct the model calibration procedure
in a more efficient way
• This methodology is limited to the process and material used
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Conclusions
Overall results
46. International ESAFORM Conference on Material Forming, April 19-21 2023, Kraków, Poland
• The hole expansion test was studied with a dual-phase steel
and an aluminium alloy
• For the steel, the most important model type was the
kinematic hardening law and the least important was the yield
function
• For the aluminum, the most important was the yield function,
whereas the least important was the kinematic hardening law
• This was expected by empirical knowledge and this automatic
strategy confirmed it
M. Conde, S. Coppieters, A. Andrade-Campos, Process-informed material model selection
Conclusions
Specific results
47. Process-informed material
model selection
Mariana Conde1,*, Sam Coppieters2, António Andrade-Campos1
1Department of Mechanical Engineering, TEMA - Centre for Mechanical
Technology and Automation, LASI – Intelligent Systems Associate
Laboratory, University of Aveiro, Portugal
2Department of Materials Engineering, KU Leuven, Belgium
*marianaconde@ua.pt
Editor's Notes
Demand of industries quality, low costs and efficiency
The development and manufacturing processes should have precise results, no delays and no waste
Virtualization and realistic simulation are required and for that it is necessary an adequate constitutive model and accurately identified parameters
Regarding the constitutive models, several models have been proposed in the literature (give examples of types,…)
Regarding the constitutive models, several models have been proposed in the literature (give examples of types,…)
Regarding the constitutive models, several models have been proposed in the literature (give examples of types,…)
Regarding the constitutive models, several models have been proposed in the literature (give examples of types,…)
Some models account for different types of mech phenomena such as Bauschinger effect, TRIP, springback,…
Some models account for different types of mech phenomena such as Bauschinger effect, springback, TRIP,…
Some models account for different types of mech phenomena such as Ratcheting, twinning,…
One thousand and three hundred combinations of models
Strategies: brute-force by comparing experimental data and find which is more adequate for a specific material and process mainly based on geometrical measurements [1], [13]–[22] and stress-strain curves or load-displacement curves and yield loci [1], [13], [15]–[18], [20]–[23]
Time-consuming-> mech experiments, model calibration, simulation and validation of mech process
Automatic&flexile tool is missing in industry and sceintific comunities
Strategies: brute-force by comparing experimental data and find which is more adequate for a specific material and process mainly based on geometrical measurements [1], [13]–[22] and stress-strain curves or load-displacement curves and yield loci [1], [13], [15]–[18], [20]–[23]
Time-consuming-> mech experiments, model calibration, simulation and validation of mech process
Automatic&flexile tool is missing in industry and sceintific comunities
The solution that we want to propose is a tool that will help simulation software users with unknown numerical material behaviour.
For instance the user wants to simulate a forming process and asks himself: How ? …? …?
He can start by looking for some models and general parameters in the literature for the material is working with.
The parameters were not calibrated exactly for the material he’s working with, but it can be adequate to detect the present mechanical phenomena.
So he can find the elastic properties, swift law, voce law, Yld2000-2d and Armstrong-Frederick model parameters for the DP600 steel.
And the same models for the aluminium alloy and their parameters
But how to get more accuracy in simulation? …? …?
This is where the proposed solution takes place.
Thus, we have a constitutive models data base to model the numerical behaviour of materials, for instance the UMMDp
We select some models
And use the material parameters from the literature
We choose the mechanical process that we want to work on and its configuration
And define the simulation specifications
With this we can do a sheet metal forming simulation
Then we can extract the some measurements of interest or critical aspects of the process
And we can use the ANOVA analysis to establish a relation between the different constitutive models and the measurements of interest
With the ANOVA results, we can establish a constitute models importance ranking
To validate this methodology we choose a hole expansion test with a blank of 0.8mm thickness
The process was simulated using Abaqus/Standard software with 3D deformable shell revolution for the blank and analytical rigid tools
In the first step, the punch is moved down with a displacement condition while the blank is fixed in the outer edge and the die is also fixed.
The imposed displacement is chosen in order to don’t reach rupture of the blank whatever the material model used.
In the second step, the tools are released and the springback is observed
A structured mesh was implemented using 6 thousand and 4 hundred S4R elements with 9 integration points along the thickness
Regarding the ANOVA approach, this is a statistical strategy that establish a relation between independent and dependent variables.
In this case, we have different types of constitutive models, such as isotropic hardening, … and different forming simulation observables such as the hole’s circularity, maximum punch force, …
We can say that the null hypothesis is that there is no difference among the group’s means
The alternative hyphothesis is that the averages are not all equal
If any group is significantly different from the overall mean, the null hypothesis is rejected. This can be observed with the p-value
The p-value is the probability of obtaining the observed results, assuming that the null hypothesis is true.
A p-value lower than 0.05 considers the statistical meaning of the analysed group.
The smaller the p-value, the more significant is the result
Thus, we simulated the hole expansion test with 8 different constitutive model combinations where we implemented either the Voce’s law or the Swift law, the von Mises of the Yld2000-2d or the kinematic A-F model, or no kinematic hardening model
These are the outputted results. Each plot has the analysed measurement of interest for each run and each material.
It can be observed that the hole’s circularity is dependent of the yld function used, as expected.
The maximum punch force is dependent of the isotropic and kinematic hardening laws, as well as the material used.
The springback factor is also dependent of both the isotropic and kinematic hardening laws.
Looking at the p-values, the greens are the values that are below 0.05 and the red are above.
For instance, it can be observed that the isotropic and kinematic hardening law have no statistical significance in the hole’s circularity.
Where as, depending on the material, the yld function can have no statistical significance in the springback factor of the steel and on the maximum punch force of the alluminium.
To better estimate the influence of each type of constitutive model in the mechanical process, we did the average of the p-values for the different measurements of interest. It can be seen that the kinematic hardening law is the model that most influences the simulation process, considering the DP600. But is the least influenceable when considering the Al.
We can look at the strain path changes using the Schmitt parameter and make similar conclusions.
The Schmitt parameters takes the value of 1 for monotonic, -1 for reversed and 0 for orthogonal strain paths.
It can be observed differences in the strain paths of the simulation using the DP.
Schmitt parameters is defined as the cosine of the angle in the strain space between the strain rate tensors during the pre-strain and subsequent strain path.
In the case of the Al, way less strain path changes are observed. This can be explained due to the smaller punch displacement imposed in the AL, compared to the DP. Different displacements were implemented because of the differences in the rupture of the materials.
Looking again at the p-values. For instance the type of model that least influences the DP simulation is the Yld function, showing the largest p-value average. On the contrary, this is the model that largest influence the simulation of the AL.
This can be confirmed by the differences in between the von Mises locus and the Yld2000-2d locus of the two materials
For the steel, …. Thus it is recommend to put more effort in the calibration of a kinematic hardening model and probably discard a complex yld function.
For the Al, … Hence, we recommend to calibrate a complex yld function and probably discard the calibration of a kinematic hardening law.