A generalized Ogden model for the compressibility of rubber-like solids

Abstract

The aim of this paper is to further demonstrate the advantages and effectiveness of the constitutive formulation proposed by Huang (Huang 2014 J. Appl. Mech. 59 , 902–908 ( doi:10.1115/1.2894059 )). In this formulation, any strain-energy function for an incompressible material can be easily generalized to include the effect of material compressibility, in which only a few material parameters and material functions to be fitted with the experimental data are required. To this end, the Ogden model for incompressible rubber-like solids is chosen as the starting point. By means of this formulation, the generalized Ogden strain-energy function, which takes into account material compressibility, can conveniently be constructed so long as its incompressible counterpart is given. The obvious advantage shown in this paper is that only a few material parameters and material functions are needed, i.e. in addition to the material parameters used in the original Ogden model for incompressible solids, only one material function depending on the volume ratio is involved to characterize the effect of compressibility. Both the material parameters in the original Ogden model and the material function suggested in this paper can be determined by fitting the experimental data for uniaxially tensile test and hydrostatic deformation test of rubbers, respectively. The present model considering compressibility is general since it can be applied to predict the stress–strain responses of rubber-like materials and porous rubbers in various loading conditions. With the present formulation, the applicable range of the celebrated Ogden model can be further broadened, which should be of practical importance for accurately describing the mechanical behaviour of rubber-like solids. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.