A constitutive model for the Mullins effect with changes in material symmetry

When an unfilled or particle reinforced rubber is subjected to cyclic loading–unloading with a fixed amplitude from its natural reference configuration, the stress required on reloading is less than on the initial loading for a deformation up to the maximum value of the stretches achieved. The stress differences in successive loading cycles are largest during the first and second cycles and become negligible after about 4–6 cycles. This phenomenon is known as the Mullins effect. In this paper new experimental data are reported showing the change in material symmetry for an initially undamaged and isotropic material subjected to uniaxial and biaxial extension tests. The effect of preconditioning in one direction on the mechanical response when loaded in a perpendicular direction is discussed. A simple phenomenological model is derived to account for stress softening and changes in material symmetry. The formulation is based on the theory of pseudo-elasticity, the basis of which is the inclusion of scalar variables in the energy function. When active, these variables modify the form of the energy function during the deformation process and therefore change the material response. The general formulation is specialized to pure homogeneous deformation in order to fit the new data. The numerical results are in very good agreement with the experimental data.