A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics

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 ${\Psi }_{nn}(F,E_0,\theta )$, $e_{nn}(F,D_0,\eta )$, ${{\rm Y}}_{nn}(F,E_0,\eta )$, or ${\Gamma }_{nn}(F,D_0,\theta )$, with $F$ representing the deformation gradient tensor, $E_0$ and $D_0$ the electric field and electric displacement field, respectively and finally, $\theta$ and $\eta$, 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 $\eta$ is typically unmeasurable. (iii) The framework accommodates models like $e_{nn}(F,D_0,\eta )$, 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.