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 b reakdown. The path integral formulation of rubber elasticity is briefly rev iewed. Within this framework the consideration of tube-like, topological co nstraints (packing effects) as well as finite chain extensibility of rubber networks is described. The results are compared to the classical Mooney-Ri vlin and inverse Langevin approaches of rubber elasticity. The effect of th e filler is taken into account via hydrodynamic reinforcement of the rubber matrix by rigid, self-similar filler clusters, which leads to a quantitati ve description of stress softening by means of a strain or pre-strain depen dent hydrodynamic amplification factor, respectively. Thereby, the pronounc ed stress softening or high hysteresis of reinforced rubber is referred to an irreversible breakdown of filler clusters during the first deformation c ycle. It is shown that the developed concept is in fair agreement with expe rimental data of unfilled NR-samples in uni-, equibiaxial and pure shear st retching mode. The pronounced stress softening of carbon black filled E-SBR - and EPDM-samples is well described on a quantitative level by an exponent ial filler cluster decay law.