Implementation of isotropic hyperelastic material models: automatic code generation in MATLAB

Abstract

With the advent of artificial intelligence and scientific machine learning, the discovery of new material models is driven at an unprecedented pace. However, integrating these novel constitutive laws into finite element analysis codes typically requires expert knowledge in different fields, including mathematics, computer science, continuum mechanics, and numerical methods. This presents a severe roadblock to the widespread adoption of these models in both research and industry. To address this challenge, a methodology for the automatic generation of user material subroutines is presented. This automated code generation process exploits MATLAB’s Symbolic (Math) Toolbox to derive closed-form expressions of the second Piola–Kirchhoff stress tensor and the fourth-order elasticity tensor directly from the strain energy density functional. The resulting expressions are automatically incorporated into a user material template previously developed by the authors. This subroutine is compatible with in-house finite element codes and, with minimal modifications, can be adapted to generate FORTRAN subroutines for use in ABAQUS. The source code is available for download from , allowing readers to immediately test and apply our methodology.