Anisotropic stress softening of electromagnetic Mullins materials

Abstract

The influence of electromagnetic forces in purely elastic deformable solids has been extensively studied in the literature. However, to the best of the author’s knowledge, the influence of electromagnetic fields on anisotropic Mullins materials has not been studied. In view of this, we propose an anisotropic phenomenological model to describe anisotropic stress softening of electromagnetic Mullins materials; 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 proposed 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 which is useful in aiding the design of a rigorous experiment to construct a specific form of constitutive equation. Since boundary value results for electromagnetic Mullins materials are not found in the literature, the effect of electromagnetic fields on the Mullins phenomena in simple tension and simple shear deformations is discussed in this paper.