Hyperelastic Constitutive Modeling of Rubber and Rubber- Like Materials under Finite Strain
Engineering and Technology Journal,
2010, Volume 28, Issue 13, Pages 2560-2575
AbstractThis paper is concerned with determining material parameters for
incompressible isotropic hyperelastic strain–energy functions. A systematic
procedure analysis is implemented based on the use of least squares optimization
method for fitting incompressible isotropic hyperelastic constitutive laws to
experimental data from the classical experiments of Treloar  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 behaviour
increases more material coefficients are required.
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