A constitutive neural network for incompressible hyperelastic materials

Abstract

We propose a B-spline-based constitutive neural network to model the mechanical behavior of incompressible isotropic materials. The theoretical foundation of this network is the Sussman-Bathe model which interpolates tension–compression test data points and recovers the strain energy function. Our neural network uses regression to self-optimize the knot configurations of the B-splines and to determine a twice differentiable curve of the material response that is closely aligned with the given data points. We address datasets displaying physically complicated behaviors. Through the patch test validation of the constitutive model and illustrative example solutions, we highlight the flexibility inherent in spline-based models and the automated approximation capabilities enabled by neural networks.