Compressible strain induced anisotropic rubberlike materials

Stress-softening in rubberlike materials is inherently anisotropic. However, most constitutive models developed in the past are isotropic models which cannot describe the anisotropic stress-softening effect, often called the Mullins effect. In this paper a phenomenological three-dimensional anisotropic constitutive equation for the Mullins effect in compressible rubberlike materials is developed. The proposed constitutive equation describes anisotropic strain induced behaviour of an initially "isotropic" virgin material. The terms, damage function and damage point, are introduced to facilitate the analysis of anisotropic stress softening in rubberlike materials. In order to develop an anisotropic stress-softening theory of compressible material in close parallel with that of incompressible material a modified right stretch tensor is used in the constitutive equation. In this way, the right stretch tensor is decompsed into its isochoric and dilatational parts. A material parametric energy function which depends on the modified right stretch tensor and pure dilatation is written explicitly in terms the of dilatation,the modified principal stretches and the principal directions of the right stretch tensor. The material parameters in the energy function are symmetric second order damage and shear-history tensors. A class of energy functions and a specific form for the constitutive equation are proposed which appear to simplify the analysis of the three-dimensional model. The proposed anisotropic theory is applied to several types of homogenous deformations, The theoretical results obtained are consistent with expected behaviour and compare well with experimental data