Publications - Mulitphysic Simulation & Optimization Lab

19274/PI/14 21996/PI/22 Analysis Applied Mathematics Computational Mathematics Computational Mechanics Computer Graphics and Computer-Aided Design Computer Science Applications Control and Optimization Control and Systems Engineering DICOPMA Dielectric elastomer Dielectric elastomers Electro-active polymer Energy–momentum scheme Evolutionary topology optimization Fail-safe design Finite element method General Engineering General Mathematics Mechanical Engineering Nonlinear electro-elasticity Numerical Analysis Ocean Engineering Phase-field PID2022-141957OA-C22 Polyconvexity Rank-one laminates Software Topology optimisation 
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2024
 Klein, Dominik;  Ortigosa, Rogelio;  Martínez-Frutos, Jesús;  Weeger, Oliver
Neural networks meet hyperelasticity: On limits of polyconvexity Journal Article Forthcoming
In: Journal of the Mechanics and Physics of Solids, Forthcoming.
BibTeX | Tags: 21996/PI/22, Computational Mechanics, Constitutive modeling, Physics-augmented machine learning, PID2022-141957OA-C22
@article{Klein2024b,

title = {Neural networks meet hyperelasticity: On limits of polyconvexity},

author = {Dominik Klein and Rogelio Ortigosa and Jesús Martínez-Frutos and Oliver Weeger},

editor = {Elsevier},

year  = {2024},

date = {2024-03-15},

urldate = {2024-03-15},

journal = {Journal of the Mechanics and Physics of Solids},

keywords = {21996/PI/22, Computational Mechanics, Constitutive modeling, Physics-augmented machine learning, PID2022-141957OA-C22},

pubstate = {forthcoming},

tppubtype = {article}

}

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2022
 Klein, Dominik K.;  Ortigosa, Rogelio;  Martínez-Frutos, Jesús;  Weeger, Oliver
Finite electro-elasticity with physics-augmented neural networks Journal Article 
In: Computer Methods in Applied Mechanics and Engineering, vol. 400, pp. 115501, 2022, ISSN: 0045-7825.
Abstract | BibTeX | Tags: Constitutive modeling, Electro-active polymers, Homogenization, Nonlinear electro-elasticity, Physics-augmented machine learning | Links: 
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@article{KLEIN2022115501,

title = {Finite electro-elasticity with physics-augmented neural networks},

author = {Dominik K. Klein and Rogelio Ortigosa and Jesús Martínez-Frutos and Oliver Weeger},

url = {https://www.sciencedirect.com/science/article/pii/S004578252200514X},

doi = {https://doi.org/10.1016/j.cma.2022.115501},

issn = {0045-7825},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {400},

pages = {115501},

abstract = {In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated as a convex neural network. In this way, the model fulfills the polyconvexity condition which ensures material stability, as well as thermodynamic consistency, objectivity, material symmetry, and growth conditions. Depending on the considered invariants, this physics-augmented machine learning model can either be applied for compressible or nearly incompressible material behavior, as well as for arbitrary material symmetry classes. The applicability and versatility of the approach is demonstrated by calibrating it on transversely isotropic data generated with an analytical potential, as well as for the effective constitutive modeling of an analytically homogenized, transversely isotropic rank-one laminate composite and a numerically homogenized cubic metamaterial. These examinations show the excellent generalization properties that physics-augmented neural networks offer also for multi-physical material modeling such as nonlinear electro-elasticity.},

keywords = {Constitutive modeling, Electro-active polymers, Homogenization, Nonlinear electro-elasticity, Physics-augmented machine learning},

pubstate = {published},

tppubtype = {article}

}

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In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated as a convex neural network. In this way, the model fulfills the polyconvexity condition which ensures material stability, as well as thermodynamic consistency, objectivity, material symmetry, and growth conditions. Depending on the considered invariants, this physics-augmented machine learning model can either be applied for compressible or nearly incompressible material behavior, as well as for arbitrary material symmetry classes. The applicability and versatility of the approach is demonstrated by calibrating it on transversely isotropic data generated with an analytical potential, as well as for the effective constitutive modeling of an analytically homogenized, transversely isotropic rank-one laminate composite and a numerically homogenized cubic metamaterial. These examinations show the excellent generalization properties that physics-augmented neural networks offer also for multi-physical material modeling such as nonlinear electro-elasticity.
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