Anisotropic modeling of the Mullins effect and the residual strain of filled silicone rubber

Many rubber like materials present a stress-softening phenomenon known as Mullins effect. It is characterized by a difference of behavior between the first and second loading and by a residual strain after a first loading. Moreover according to the literature this stress softening is anisotropic. A new constitutive equation is proposed. It relies on the decomposition of the macromolecular network into two parts: chains related together and chains related to fillers. The first part is modeled by a simple hyperelastic constitutive equation whereas the second one is described by a constitutive equation describing both the anisotropic stress softening and the residual strain. A 42 directions discretization is chosen to describe the anisotropic part of the model. An evolution function is introduced in the constitutive equation in each direction to record the history of the material. The equations are written by means of strain invariants in order to build a model easy to implement in a finite element code. The constitutive equation is finally validated on experimental data.