Mixture of Polyconvex Neural Potentials for Parametric Hyperelasticity: Towards Foundation Material Models

Abstract

Hyperelastic constitutive models enable modeling large deformations in elastic solids. In common practice, a strain energy density function is prescribed in advance and model-specific parameters are calibrated from experiments. However, many applications require constitutive models for a family of related materials whose mechanical behavior varies with composition. A fixed constitutive model-form may not capture the full range of behavior across the family, while fitting separate forms does not provide a direct way to predict the response of new compositions. Recent work has developed data-driven constitutive models that learn flexible strain energy functions while incorporating key physical constraints. In this work, we propose using mixtures of convex neural potentials based on input convex neural networks as a modular and data efficient approach to modeling material families. Each potential is convex and monotonic with respect to polyconvex strain invariants, while a conditioning network maps material descriptors to mixture weights. We compare the approach with a monolithic partially input-convex neural network using experimental data from PolyJet 3D-printed materials and a synthetic Gent-type benchmark. Across both benchmarks, the mixture architecture generalized better to material descriptors not seen during training. In the PolyJet experimental benchmark, we showed that the mixture architecture is less sensitive to model hyperparameters, while in the Gent-type benchmark it generalized more reliably with sparse data in the material-descriptor space. These results suggest that representing a material family through a small set of shared convex neural potentials provides a useful structural prior for learning descriptor-dependent constitutive behavior from limited data.