Hyperelastic Constitutive Modeling of Rubber and Rubber- Like Materials under Finite Strain

This paper is concerned with determining material parameters forincompressible isotropic hyperelastic strain–energy functions. A systematicprocedure analysis is implemented based on the use of least squares optimizationmethod for fitting incompressible isotropic hyperelastic constitutive laws toexperimental data from the classical experiments of Treloar [3] on natural rubber.Two phenomenological constitutive models are used to fit the experimental dataof natural rubber, these are Mooney-Rivlin and Ogden models. The materialparameters using Mooney-Rivlin are obtained using the linear least squaresmethod, while for Ogden model the material coefficients are nonlinear,consequently the nonlinear least squares approach has been used. In this work thenonlinear least squares method with trusted region TD have been used usingMATLAB Ver. 7 to find these coefficients. The comparison shows that the presentmathematical formulations are correct and valid for modeling rubbery materials.Also it was found that Mooney-Rivlin model is suitable when the deformation isnot to exceed 100%, while Ogden model is more appropriate when deformationexceed 100%. In addition, as the degree of non-linearity in material behaviourincreases more material coefficients are required.