Anisotropic stress softening of residually stressed solids

Residual stress in purely elastic solids has been extensively studied in the literature. However, to the best of the author's knowledge, the influence of residual stresses on anisotropic Mullins materials has not been studied. Hence, the aim of this paper is to propose an anisotropic phenomenological model to describe the Mullins phenomena for residually stressed elastomers; taking note that most materials are not purely elastic and some of them exhibit an anisotropic stress-softening phenomenon widely known as the Mullins effect. The anisotropic model is based on the use of direction-dependent damage parameters and a set of anisotropic spectral invariants presented recently in the literature by the author. The spectral invariants have a clear physical meaning that is useful in aiding the design of a rigorous experiment to construct a specific form of constitutive equation. Since boundary value results for residually stressed Mullins material are not found in the literature, the effect of residual stresses on the Mullins phenomena in simple tension, torsion and equibiaxial deformations is discussed in this paper.