23 Apr 2024 | Jan N. Fuhg, Asghar Jadooon, Oliver Weeger, D. Thomas Seidl, Reese E. Jones
This paper presents a polyconvex neural network framework for thermoelasticity, which extends a previously developed hyperelastic neural network to account for temperature effects. The framework incorporates thermodynamic and material-theoretic constraints to ensure polyconvexity with respect to deformation and concavity with respect to temperature. The neural network is trained using a sparsification algorithm that prevents overfitting and promotes generalization. The model is validated on synthetic data and experimental datasets, demonstrating its ability to accurately predict thermomechanical behavior, including thermal expansion, thermal softening, and thermal inversion. The framework is capable of representing non-self-similar temperature dependence and general thermal phenomena. The model is implemented using physics-constrained neural networks, which are calibrated with a sparsification algorithm to ensure accurate and interpretable results. The results show that the model can generalize well to unseen data and accurately capture the expected thermomechanical responses. The framework is also applicable to anisotropic thermo-hyperelasticity through the inclusion of additional invariants associated with a structure tensor. The study highlights the potential of machine learning in modeling complex thermomechanical behaviors with physical constraints.This paper presents a polyconvex neural network framework for thermoelasticity, which extends a previously developed hyperelastic neural network to account for temperature effects. The framework incorporates thermodynamic and material-theoretic constraints to ensure polyconvexity with respect to deformation and concavity with respect to temperature. The neural network is trained using a sparsification algorithm that prevents overfitting and promotes generalization. The model is validated on synthetic data and experimental datasets, demonstrating its ability to accurately predict thermomechanical behavior, including thermal expansion, thermal softening, and thermal inversion. The framework is capable of representing non-self-similar temperature dependence and general thermal phenomena. The model is implemented using physics-constrained neural networks, which are calibrated with a sparsification algorithm to ensure accurate and interpretable results. The results show that the model can generalize well to unseen data and accurately capture the expected thermomechanical responses. The framework is also applicable to anisotropic thermo-hyperelasticity through the inclusion of additional invariants associated with a structure tensor. The study highlights the potential of machine learning in modeling complex thermomechanical behaviors with physical constraints.