Learning a hyperelastic constitutive model from 3D experimental data

A hyperelastic constitutive law is experimentally learned and validated from three-dimensional full-field kinematic data. 3D-printed thermoplastic polyurethane specimens were subjected to monotonic uniaxial tension within a laboratory micro-computed tomography system. Global Digital Volume Correlation yields volumetric displacement fields, reaching up to 35% axial strain. A Physics-Augmented Neural Network (PANN) architecture, embedding polyconvexity constraints through an input-convex neural network, is trained in an unsupervised manner by enforcing mechanical equilibrium via the EUCLID loss, using only measured displacements and global reaction forces. This three-dimensional formulation eliminates the need for depth-related assumptions inherent in 2D measurements and provides improved representation of boundary conditions, which is critical for equilibrium-based training. For comparison, Neo-Hookean and Saint-Venant-Kirchhoff models are identified in parallel. The PANN achieves superior equilibrium satisfaction, outperforming both linear and Neo-Hookean benchmarks. In addition to the original specimen, a second experiment on a different sample was performed under comparable loading conditions. This configuration provides an independent validation dataset acquired under slightly varying experimental conditions, thereby testing the robustness and transferability of the learned constitutive model. This work presents the first experimental demonstration of unsupervised PANN model training and establishes a practical protocol for data-based hyperelastic characterization from volumetric measurements.