Polyconvex Neural Network Models of Thermoelasticity

Polyconvex Neural Network Models of Thermoelasticity

23 Apr 2024 | Jan N. Fuhr, Asghar Jadoon, Oliver Weeger, D. Thomas Seidl, Reese E. Jones
This paper presents a novel framework for modeling thermo-hyperelastic materials using machine learning, specifically neural networks. The authors extend a polyconvex hyperelastic neural network framework to incorporate thermomechanical principles, ensuring that the free energy function is polyconvex with respect to deformation and concave with respect to temperature. The proposed framework is calibrated using a sparsification algorithm that penalizes the number of active parameters to prevent overfitting and promote generalization. The performance of the framework is demonstrated on synthetic data and experimental datasets, showing its ability to accurately predict thermomechanical phenomena such as thermal expansion, thermal softening, and thermal inversion. The paper also discusses the physical constraints and mathematical foundations of thermo-hyperelasticity, providing a comprehensive overview of the theoretical and computational aspects.This paper presents a novel framework for modeling thermo-hyperelastic materials using machine learning, specifically neural networks. The authors extend a polyconvex hyperelastic neural network framework to incorporate thermomechanical principles, ensuring that the free energy function is polyconvex with respect to deformation and concave with respect to temperature. The proposed framework is calibrated using a sparsification algorithm that penalizes the number of active parameters to prevent overfitting and promote generalization. The performance of the framework is demonstrated on synthetic data and experimental datasets, showing its ability to accurately predict thermomechanical phenomena such as thermal expansion, thermal softening, and thermal inversion. The paper also discusses the physical constraints and mathematical foundations of thermo-hyperelasticity, providing a comprehensive overview of the theoretical and computational aspects.
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