An anisotropic model of the Mullins effect

The Mullins effect in rubber-like materials is inherently anisotropic. However, most constitutive models developed in the past are isotropic. These models cannot describe the anisotropic stress-softening effect, often called the Mullins effect. In this paper a phenomenological three-dimensional anisotropic model for the Mullins effect in incompressible rubber-like materials is developed. The terms, damage function and damage point, are introduced to facilitate the analysis of anisotropic stress softening in rubber-like materials. A material parametric energy function which depends on the right stretch tensor and written explicitly in terms of principal stretches and directions is postulated. 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 both the analysis of the three-dimensional model and the calculation of material constants from experimental data. The behaviour of tensional and compressive ground-state Young’s moduli in uniaxial deformations is discussed. To further justify our model we show that the proposed model produces a transversely anisotropic non-virgin material in a stress-free state after a simple tension deformation. The proposed anisotropic theory is applied to several types of homogenous deformations and the theoretical results obtained are consistent with expected behaviour and compare well with several experimental data.