Modeling Hyperelastic Materials by MATLAB

Abstract

The finite element studies of hyperelastic materials always need founding a mathematical model describes the behavior of their elements. Several constitutive models differ in matching accuracy, can describe the behavior of hyperelastic material, such as Neo-Hookean, Yeoh, and Mooney-Rivlin, which are all derived from the strain energy density function. Founding a mathematical model describing the behavior of some hyperelastic material means the determination of the constitutive model's invariants, which are considered as material parameters. In this work, the two-parameter Mooney-Rivlin model was chosen to demonstrate the procedure of forming the mathematical model that describes the mechanical behavior of an incompressible hyperelastic material. Comparing with those results taken from Abaqus, obtained results were very close and exhibited a lower absolute error. This procedure can be considered as a general method to describe the hyperelastic materials by the other polynomial constitutive models.