Automated discovery of effective material models for nonhomogeneous hyperelastic materials

This paper presents an automated framework based on first-order Cauchy elasticity theory, which aims to identify effective material models of nonhomogeneous hyperelastic materials. The method utilizes full-scale finite element simulations of representative volume elements to predict the effective properties of materials at the macroscale. A comprehensive feature library is employed to represent the hyperelastic strain energy density, incorporating functions in terms of isotropic and anisotropic invariants. The coefficients of these features are obtained by solving a constrained optimization problem that simultaneously enforces the equilibrium equations, reaction forces, and strain energy function. The optimization strategy incorporates uniaxial, biaxial, and shear loading under strain and stress control conditions within the objective function. The framework's primary strength lies in its adaptability, which allows it to accommodate nonlinear base materials with anisotropic microstructures. In order to identify the invariants as known values within this framework, an isogeometric discretization enhances numerical precision by offering higher-order smoothness. This enables the calculation of the homogenized deformation gradient across each volume element.A comprehensive comparison study is conducted to evaluate the predicted homogenized strain energy and stress-strain behavior under various loading conditions. It demonstrates close agreement with full-scale simulations, thereby substantiating the approach's reliability and validity. Microstructures constituted of two distinct base materials, Neo-Hooke and Mooney-Rivlin, serve as benchmark examples, illustrating the robustness of the approach under varying inclusion contrasts. Beyond standard material parameters, this automated framework also has potential applications for nonlinear material parameters or neural network-based constitutive models.