An anisotropic model for the Mullins effect in rubber

Mullins effect in rubberlike materials is inherently anisotropic. However, most constitutive models developed in the past are isotropic models which cannot describe the anisotropic behaviour of Mullins effect. In this paper we develop a phenomenological three dimensional nonlinear anisotropic model for the Mullins effect in incompressible rubberlike materials. Primary and secondary strain-magnitude-damage measures together with their unloading points are defined. A parametric energy function which depends on the right stretch tensor is postulated. The parameters in the energy function are unloading points and shear parameters. A specific form for the constitutive equation is proposed which appears to simplify both the analysis of the three dimensional model and the calculation of material constants from experimental data. We show, as physically expected, that the proposed model produces a transversely anisotropic non-virgin material in a stress free state after a uniaxial deformation. The proposed model gives reasonable results for several homogeneous deformations that induced anisotropic stress-softening. The theoretical results compare well with several experimental data.