HyperSym: a MATLAB code for symbolic differentiation of ready-to-use tensors in hyperelastic finite element analysis

Abstract

Implementing nonlinear material models, such as hyperelasticity, in finite element software can be a  daunting task for engineering students due to the complexities of transitioning from linear to nonlinear analysis  and the interdisciplinary knowledge required, including tensor calculus, programming, and continuum mechanics.  To address these challenges, we present HyperSym, an educational MATLAB-based tool designed to simplify the implementation of hyperelastic material models. HyperSym leverages symbolic differentiation to derive hyperelastic tensors from strain energy density functions, generating ready-to-use subroutines that integrate seamlessly  with the open-source NLFEA finite element framework. This paper highlights HyperSym’s core functionality, demonstrates its educational value through a numerical example suitable for lectures and assignments, and provides access to the complete MATLAB implementation via a public repository.