  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.
