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2025
 Ortigosa, Rogelio;  Martínez-Frutos, Jesús;  Pérez-Escolar, Alberto;  Castañar, Inocencio;  Ellmer, Nathan;  Gil, Antonio J.
A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics Journal Article 
In: Computer Methods in Applied Mechanics and Engineering, vol. 437, pp. 117741, 2025, ISSN: 0045-7825.
Abstract | BibTeX | Tags: Dielectric elastomers, Finite elements, Machine learning, Neural networks, PID2022-141957OA-C22, Thermo-electro-mechanics | Links: 
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@article{ORTIGOSA2025117741,

title = {A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Alberto Pérez-Escolar and Inocencio Castañar and Nathan Ellmer and Antonio J. Gil},

url = {https://www.sciencedirect.com/science/article/pii/S0045782525000131},

doi = {https://doi.org/10.1016/j.cma.2025.117741},

issn = {0045-7825},

year  = {2025},

date = {2025-01-01},

urldate = {2025-01-01},

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

volume = {437},

pages = {117741},

abstract = {This manuscript introduces a novel neural network-based computational framework for constitutive modeling of thermo-electro-mechanically coupled materials at finite strains, with four key innovations: (i) It supports calibration of neural network models with various input forms, such as Ψnn(F,E0,θ), enn(F,D0,η), Υnn(F,E0,η), or Γnn(F,D0,θ), with F representing the deformation gradient tensor, E0 and D0 the electric field and electric displacement field, respectively and finally, θ and η, the temperature and entropy fields. These models comply with physical laws and material symmetries by utilizing isotropic or anisotropic invariants corresponding to the material’s symmetry group. (ii) A calibration approach is developed for the case of experimental data, where entropy η is typically unmeasurable. (iii) The framework accommodates models like enn(F,D0,η), specially convenient for the imposition of polyconvexity across the three physics involved. A detailed calibration study is conducted evaluating various neural network architectures and considering a large variety of ground truth thermo-electro-mechanical constitutive models. The results demonstrate excellent predictive performance on larger datasets, validated through complex finite element simulations using both ground truth and neural network-based models. Crucially, the framework can be straightforwardly extended to scenarios involving other physics.},

keywords = {Dielectric elastomers, Finite elements, Machine learning, Neural networks, PID2022-141957OA-C22, Thermo-electro-mechanics},

pubstate = {published},

tppubtype = {article}

}

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This manuscript introduces a novel neural network-based computational framework for constitutive modeling of thermo-electro-mechanically coupled materials at finite strains, with four key innovations: (i) It supports calibration of neural network models with various input forms, such as Ψnn(F,E0,θ), enn(F,D0,η), Υnn(F,E0,η), or Γnn(F,D0,θ), with F representing the deformation gradient tensor, E0 and D0 the electric field and electric displacement field, respectively and finally, θ and η, the temperature and entropy fields. These models comply with physical laws and material symmetries by utilizing isotropic or anisotropic invariants corresponding to the material’s symmetry group. (ii) A calibration approach is developed for the case of experimental data, where entropy η is typically unmeasurable. (iii) The framework accommodates models like enn(F,D0,η), specially convenient for the imposition of polyconvexity across the three physics involved. A detailed calibration study is conducted evaluating various neural network architectures and considering a large variety of ground truth thermo-electro-mechanical constitutive models. The results demonstrate excellent predictive performance on larger datasets, validated through complex finite element simulations using both ground truth and neural network-based models. Crucially, the framework can be straightforwardly extended to scenarios involving other physics.
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