On the development of compressible pseudo-strain energy density function for elastomers: Part 1. Theory and experiment

This study was carried out to develop a compressible pseudo-strain energy function that describes the mechanical behavior of rubber-like materials. The purpose of this work is two-fold; first is to define a single term strain energy function derived from constitutive equations that can describe the mechanical behavior of rubber-like materials, taking into account the coupling between principal stretches and the near incompressibility characteristic of elastomers. Second is to implement this strain energy function into finite element method (FEM) to reduce the computational time. A one-term three-dimensional strain energy density 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 conditions, based on membrane theory. The work presented herein was based on the decoupling of the strain energy density function into deviatoric and volumetric parts. 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 parameter of the proposed strain energy function. A genetic algorithm (GA) curve fitting technique was utilized in 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 predicts the mechanical behavior of rubber-like material with greater accuracy as compared to other well-known models.