@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}

}

@article{HORAK2023115695,

title = {A polyconvex transversely-isotropic invariant-based formulation for electro-mechanics: Stability, minimisers and computational implementation},

author = {Martin Horák and Antonio J. Gil and Rogelio Ortigosa and Martin Kružík},

url = {https://www.sciencedirect.com/science/article/pii/S0045782522006508},

doi = {https://doi.org/10.1016/j.cma.2022.115695},

issn = {0045-7825},

year  = {2023},

date = {2023-01-01},

urldate = {2023-01-01},

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

volume = {403},

pages = {115695},

abstract = {The use of Electro-Active Polymers (EAPs) for the fabrication of evermore sophisticated miniaturised soft robotic actuators has seen an impressive development in recent years. The incorporation of crystallographic anisotropic micro-architectures, within an otherwise nearly uniform isotropic soft polymer matrix, has shown great potential in terms of advanced three-dimensional actuation (i.e. stretching, bending, twisting), especially at large strains, that is, beyond the onset of geometrical pull-in instabilities. From the computational point of view, the design of accurate and robust albeit efficient constitutive models is a very active area of research. This paper introduces a novel polyconvex phenomenological invariant-based transversely isotropic formulation (and relevant computational frameworks) for the simulation of transversely isotropic EAPs at large strains, where the ab initio satisfaction of polyconvexity is exploited to ensure the robustness of numerical results for any range of deformations and applied electric fields. The paper also presents key important results both in terms of the existence of minimisers and material stability of coupled electro-mechanics, enhancing previous works in the area of large strain elasticity. In addition, a comprehensive series of selected numerical examples is included in order to demonstrate the effect that the anisotropic orientation and the contrast of material properties, as well as the level of deformation and electric field, have upon the response of the EAP when subjected to large three-dimensional stretching, bending and torsion, including the possible development of wrinkling and the potential loss of ellipticity in ill-posed constitutive models.},

keywords = {Dielectric elastomers, Electro-elasticity, Finite element method, Polyconvexity, Transversely isotropic},

pubstate = {published},

tppubtype = {article}

}

@article{FRANKE2022114298,

title = {A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics},

author = {M. Franke and Rogelio Ortigosa and Jesús Martínez-Frutos and Antonio J. Gil and P. Betsch},

url = {https://www.sciencedirect.com/science/article/pii/S0045782521005922},

doi = {https://doi.org/10.1016/j.cma.2021.114298},

issn = {0045-7825},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

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

volume = {389},

pages = {114298},

abstract = {The aim of this paper is the design of a new one-step implicit and thermodynamically consistent Energy–Momentum (EM) preserving time integration scheme for the simulation of thermo-electro-elastic processes undergoing large deformations. The time integration scheme takes advantage of the notion of polyconvexity and of a new tensor cross product algebra. These two ingredients are shown to be crucial for the design of so-called discrete derivatives fundamental for the calculation of the second Piola–Kirchhoff stress tensor, the entropy and the electric field. In particular, the exploitation of polyconvexity and the tensor cross product, enable the derivation of comparatively simple formulas for the discrete derivatives. This is in sharp contrast to much more elaborate discrete derivatives which are one of the main downsides of classical EM time integration schemes. The newly proposed scheme inherits the advantages of EM schemes recently published in the context of thermo-elasticity and electro-mechanics, whilst extending to the more generic case of nonlinear thermo-electro-mechanics. Furthermore, the manuscript delves into suitable convexity/concavity restrictions that thermo-electro-mechanical strain energy functions must comply with in order to yield physically and mathematically admissible solutions. Finally, a series of numerical examples will be presented in order to demonstrate robustness and numerical stability properties of the new EM scheme.},

keywords = {DICOPMA, Dielectric elastomers, Electro active polymers, Energy–momentum scheme, Finite element method, Nonlinear thermo-electro-elastodynamics, Polyconvexity, Tensor cross product},

pubstate = {published},

tppubtype = {article}

}