Learning a hyperelastic constitutive model from 3D experimental data
Year: 2025
Type: article
Abstract: A hyperelastic constitutive law is experimentally learned and validated from three-dimensional full-field kinematic data. A 3D-printed thermoplastic polyurethane specimen is subjected to monotonic uniaxial tension within a laboratory micro-computed tomography system. Global Digital Volume Correlation yields volumetric displacement fields at four load levels, 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, with mean absolute internal force residuals below 0.8 N across unseen loading steps, outperforming both linear and Neo-Hookean benchmarks. This work presents the first experimental demonstration of unsupervised 3D PANN model training and establishes a practical protocol for data-driven hyperelastic characterization from volumetric measurements.
Authors: M. Bourdyot, M. Compans, R. Langlois, B. Smaniotto, E. Baranger, C. Jailin
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,830
Funder: Agence Nationale de la Recherche
Award: G4962797873
OpenAlex ID: W4417281535