Analysis of the isotropic models of the Mullins effect based on filled silicone rubber experimental results

The Mullins effect of rubber-like material is classically defined as the stress softening during initial loading cycles. This effect is not accounted when the mechanical properties of material are modeled by a simple hyperelastic strain-energy function. In order to capture the stress softening it is necessary to define a set of supplementary variables as well as a dissipation function, which evolves with the deformation history. In this paper, we first describe experimental results that illustrate stress softening in particle-reinforced silicone rubber for uniaxial, planar and equibiaxial tensile tests. The results allow to analyze the stress softening for the three different load cases. First, with respect to the choice of a stress-softening measure, the energy loss is evaluated by comparing the stored elastic energy for the first and the second loadings. The results point out that the virgin energy and the first invariant parameters are the best choice. Nevertheless, the maximum principal elongation, classically used in Mullins effect modeling, is not able to describe the different load cases. Furthermore, the ability of different class of models to describe filled silicone rubber is studied. The results show that models with a non-proportional and non-homothetical second load paths seem to be more efficient.