Modelling dilatational stress softening of rubber

This study is concerned with experimental and numerical aspects of dilatational stress softening, a phenomenon observed in unfilled as well as carbon-black filled elastomers when subjected to tensile hydrostatic loading of sufficient magnitude. It has long been known that rubber subjected to hydrostatic tensile stress causes internal rupture or cavitation with a corresponding permanent reduction of the tensile bulk modulus. In particular, we examine experimental results for unfilled rubber, which highlight a sudden elastic instability and a corresponding change in the value of the bulk modulus during hydrostatic loading and a significant stress softening that occurs during unloading and subsequent reloading. Dilatational stress softening and the accumulation of residual volumetric change upon complete unloading are not accounted for when the material is modelled as hyperelastic. In this paper we treat the elastomer as a compressible pseudo-elastic material and focus on the dilatational part of the strain energy function. We suggest a simple constitutive approach to account for stress softening and the accumulation of residual volumetric change by introducing a damage variable, which provides a means for modifying the volumetric strain energy function to reflect stress softening during unloading and subsequent reloading.