The Mullins effect in compressible solids

A general constitutive theory of stress-softening in isotropic, compressible materials based on a two phase microstructural damage model is presented. Stress-softening induced by an uniaxial stretch of the material is analyzed, and some general analytical results consonant with experimental observations are obtained. It is shown for compressible stress-softening materials that the Poisson function for the elastic stress-softened material generally will differ from that for the virgin material. Some general characteristics of the physical response of equi-Poisson materials are described, and an example of a general class of these materials is presented. It is shown that the physical response of isotropic, compressible stress-softening materials parallels that described in earlier papers on its incompressible counterpart. For illustration, a special subclass of stress-softening hyperelastic parent materials and an exponential softening function are introduced. The general results are then described graphically for uniaxial tension and compression of a special class of Blatz–Ko parent material models developed from experiments on polyurethane foamed rubbers.