Hyperelastic constitutive modeling of rubber and rubber-like materials under finite strain

Abstract EN

This paper is concerned with determining material parameters for incompressible isotropic hyper elastic strain–energy functions.

A systematic procedure analysis is implemented based on the use of least squares optimization method for fitting incompressible isotropic hyper elastic constitutive laws to experimental data from the classical experiments of Treloar [3] on natural rubber.

Two phenomenological constitutive models are used to fit the experimental data of natural rubber, these are Mooney-Rivlin and Ogden models.

The material parameters using Mooney-Rivlin are obtained using the linear least squares method, while for Ogden model the material coefficients are nonlinear, consequently the nonlinear least squares approach has been used.

In this work the nonlinear least squares method with trusted region TD have been used using MATLAB Ver.

7 to find these coefficients.

The comparison shows that the present mathematical formulations are correct and valid for modeling rubbery materials.

Also it was found that Mooney-Rivlin model is suitable when the deformation is not to exceed 100%, while Ogden model is more appropriate when deformation exceed 100%.

In addition, as the degree of non-linearity in material behavior increases more material coefficients are required.