ON THE DEVELOPMENT OF COMPRESSIBLE PSEUDO-STRAIN ENERGY DENSITY FUNCTION FOR HYPERELASTIC MATERIAL: EXPERIMENT, THEORY AND FEM

Abstract

This study was carried out to develop a compressible pseudo-strain energy function that describes the mechanical behavior of rubber-like materials. The motivation for this work was two fold; first was to define a single-term strain energy function derived from constitutive equations that can describe the mechanical behavior of rubber-like materials and taking into account the coupling between principal stretches and the nearly incompressibility characteristic of elastomers. Second was to implement this strain energy function into the Finite Element Method (FEM) to study the suitability of the model in FEM. A one-term three-dimensional strain energy function based on the principal stretch ratios was proposed. The three dimensional constitutive function was then reduced to describe the behavior of rubber-like materials under biaxial and uniaxial loading condition based on the membrane theory. The work presented here was based on the decoupling of the strain density function into a deviatoric and a volumetric part. Using pure gum, GMS-SS-A40, uniaxial and equi-biaxial experiments were conducted employing different strain rate protocols. The material was assumed to be isotropic and homogenous. The experimental data from uniaxial and biaxial tests were used simultaneously to determine the material parameters of the proposed strain energy function. A GA curve fitting technique was utilized in the material parameter identification. The proposed strain energy function was compared to a few well-known strain energy functions as well as the experimental results. It was determined that the proposed strain energy function predicted the mechanical behavior of rubber-like material with greater accuracy as compared to other models both analytical and numerical results.