Theory and identification of a constitutive model of induced anisotropy by the Mullins effect

Abstract

Rubber-like materials present a stress softening phenomenon after a first loading known as the Mullins effect. Some recent experimental data on filled silicone rubber are presented in the literature, using uniaxial and biaxial tests to precondition samples thus induce some primary stress softening. A generic modeling based on the polymer network decomposition into an isotropic hyperelastic one, and a stress-softening evolutive one, is proposed taking into account the contribution of many spatial directions. A new stress softening criterion is built by means of a tensor that measures the repartition of energy in space. A general form of the stress softening function associated to a spatial direction is written by the way of two variables: one, the maximal eigenvalue of the energy tensor; the other, the energy in the considered direction. Finally, a particular form of constitutive equation is proposed. The model is fitted and compared to experimental data. The capacities of such modeling are finally discussed.