Generalized invariants meet constitutive neural networks: A novel framework for hyperelastic materials

TL;DR

This paper presents a neural network framework that automatically discovers suitable invariants and constitutive models for hyperelastic materials directly from experimental data, improving flexibility and interpretability.

Contribution

It introduces a unified neural network approach that simultaneously identifies invariants and strain energy functions for hyperelastic materials from data.

Findings

Successfully applied to rubber and brain tissue datasets

Recovers classical models for rubber and nonlinear responses for brain tissue

Outperforms traditional models in predictive accuracy and interpretability

Abstract

The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven framework that simultaneously discovers appropriate invariants and constitutive models for isotropic incompressible hyperelastic materials. Our approach identifies both the most suitable invariants in a class of generalized invariants and the corresponding strain energy function directly from experimental observations. Unlike previous methods that rely on fixed invariant choices or sequential fitting procedures, our method integrates the discovery process into a single neural network architecture. By looking at a continuous family of possible invariants, the model can flexibly adapt to different material behaviors. We demonstrate the effectiveness of this approach using popular benchmark datasets for rubber and brain tissue. For rubber, the method recovers a stretch-dominated formulation consistent with classical models. For brain tissue, it identifies a formulation sensitive to small stretches, capturing the nonlinear shear response characteristic of soft biological matter. Compared to traditional and neural-network-based models, our framework provides improved predictive accuracy and interpretability across a wide range of deformation states. This unified strategy offers a robust tool for automated and physically meaningful model discovery in hyperelasticity.