Identifying constitutive parameters for complex hyperelastic materials using physics-informed neural networks

Abstract

Identifying constitutive parameters in engineering and biological materials, particularly those with intricate geometries and mechanical behaviors, remains a longstanding challenge. The recent advent of physics-informed neural networks (PINNs) offers promising solutions, but current frameworks are often limited to basic constitutive laws and encounter practical constraints when combined with experimental data. In this paper, we introduce a robust PINN-based framework designed to identify material parameters for soft materials, specifically those exhibiting complex constitutive behaviors, under large deformation in plane stress conditions. Distinctively, our model emphasizes training PINNs with multi-modal synthetic experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even with noisy data. Our results reveal that the PINNs framework can accurately identify constitutive parameters of the incompressible Arruda–Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%. We believe our framework provides a robust modulus identification approach for complex solids, especially for those with geometrical and constitutive complexity.