ABSTRACT
The non-affine microsphere model based on network free energy minimization under the maximal advance path kinematic constraint, has been extended to account for possible chain length distribution, and damage such as Mullins softening observed in filled rubber materials. When considering the isotropic hyperelastic behavior of rubberlike materials presenting chains of various lengths, the resulting equal-force model shows an improved deformability compared to the affine model that is limited by the maximum extension of the shorter chains, and a significantly softer behavior. To reproduce Mullins softening, damage was introduced by increasing the chain lengths according to the submitted maximal chain traction force. The damage is applied on each chain independently, resulting in a directional softening that introduces an evolution of the stress-free configuration that has to be assessed over the loadings. The model is shown to reproduce well the cyclic uniaxial tension behavior of a filled styrene butadiene rubber to feature Mullins induced anisotropy.
