Polyconvex neural network models of thermoelasticity

TL;DR

This paper develops neural network models for thermoelasticity that incorporate thermodynamic constraints, ensuring physically consistent behavior, and demonstrates their effectiveness on synthetic and experimental data.

Contribution

It extends polyconvex hyperelastic neural networks to thermo-hyperelasticity with thermodynamic constraints and introduces a sparsification algorithm for better generalization.

Findings

Successfully modeled thermomechanical phenomena with synthetic data

Accurately fit temperature-dependent experimental datasets

Ensured physical consistency through thermodynamic constraints

Abstract

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.