Influence of Material Non Homogeneity on the Shearing Response of a Neo Hookean Slab

Abstract

Abstract Vulcanized rubber components possess material non-homogeneities due to either non-uniform vulcanization during their fabrication or attack of thermal and oxidative environments during their service life. The primary objective of this paper is to theoretically investigate the effect of a material non-homogeneity on the shearing response of an isotropic, incompressible neo-Hookean slab. The non-homogeneity considered in the slab is the spatially varying shear modulus that is approximately described by a spatial-distribution function. A parabolic and a boundary layer-like spatial-distribution function are assumed; then exact solutions for the stress—strain fields in the slab are obtained by solving the linear momentum balance equations based on a postulated inhomogeneous shearing deformation. Our theoretical results show that the shear strain is more inhomogeneous and localized for the slabs with a greater degree of spatial non-homogeneity. In the non-homogeneous slabs, we have also determined the existence of a uniform shear stress and an inhomogeneous first normal-stress difference whose variation is similar to that of the shear strain. The implications of these results are considered in terms of the fabrication, performance and mechanical characterization of the rubber-elastic materials.