An averaging based tube model for deformation induced anisotropic stress softening of filled elastomers

In this paper, a micromechanically based constitutive model capturing anisotropic stress softening in reinforced elastomers under quasi-static loading is presented. A novel spatial distribution function of polymer chains taking into account its deformation induced anisotropic alignment is proposed. By this means, the anisotropic network averaging over the unit sphere can be evaluated analytically. The anisotropic alignment of polymer chains introduces non-affine deformation in the model. Furthermore, the anisotropic evolution of the Mullins effect and hysteresis are also derived analytically, so that no numerical integration is applied here. The model includes very few physically motivated material parameters and demonstrates good agreement with multi-dimensional experimental data as well as with molecular dynamics simulations.