A generalized tube model of rubber elasticity and stress softening of filler reinforced elastomer systems

An advanced micro-mechanical model of hyperelasticity and stress softening of reinforced rubbers is presented that combines a non-Gaussian tube model of rubber elasticity with a damage model of stress-induced filler cluster breakdown. The path integral formulation of rubber elasticity is briefly reviewed. Within this framework the consideration of tube-like, topological constraints (packing effects) as well as finite chain extensibility of rubber networks is described. The results are compared to the classical Mooney-Rivlin and inverse Langevin approaches of rubber elasticity. The effect of the filler is taken into account via hydrodynamic reinforcement of the rubber matrix by rigid, self-similar filler clusters, which leads to a quantitative description of stress softening by means of a strain or pre-strain dependent hydrodynamic amplification factor, respectively. Thereby, the pronounced stress softening or high hysteresis of reinforced rubber is referred to an irreversible breakdown of filler clusters during the first deformation cycle. It is shown that the developed concept is in fair agreement with experimental data of unfilled NR-samples in uni-, equibiaxial and pure shear stretching mode. The pronounced stress softening of carbon black filled E-SBR- and EPDM-samples is well described on a quantitative level by an exponential filler cluster decay law.