Work

Learning shared hyperelastic constitutive representation from heterogeneous full-field experiments across multiple materials

Year: 2026

Type: article

Abstract: A Physics-Augmented Neural Network is introduced to learn a shared isotropic hyperelastic constitutive representation from full-field experiments on several material families. Each experimental instance is assigned a spatially homogeneous constitutive law at the modeling scale, while deformation may be heterogeneous. Both nearly incompressible and compressible responses are considered, namely, an isochoric kinematic completion is used for two-dimensional displacement data, whereas three-dimensional bulk data retain measured volume changes. The complete database comprises 30 experiments quantified by image correlation on various materials such as elastomers, cork, foam, and architected metamaterials. The database includes several specimen geometries, loading paths, mesh resolutions, and measurement modalities. The model consists of a shared input-convex backbone that maps strain invariants to convex energy modes. Material dependence is introduced only through non-negative modal amplitudes, yielding a compact constitutive embedding while preserving a common admissible backbone. Among the investigated embedding dimensions, the four-mode representation provides the best post-calibration performance, which corresponds to a reduction of 66% relative to independently calibrated Neo-Hookean models, while remaining less accurate than independently trained single-dataset PANNs. The learned amplitudes exhibit family-level organization in exploratory low-dimensional projections. The frozen backbone further enables reduced calibration of experimental instances withheld from backbone training, using only four non-negative coefficients. These results show that heterogeneous full-field experiments can be used collectively to learn a reusable, physically constrained constitutive basis, rather than being only treated as independent identification problems.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2026.119498