Hyperelasticity and stress softening of filler reinforced polymer networks

Starting from an analysis of filler networking in bulk polymers, a constitutive micro-mechanical model of stress softening and hysteresis of filler reinforced polymer networks is developed. It refers to a non-affine tube model of rubber elasticity, including hydrodynamic amplification of the rubber matrix by a fraction of hard, rigid filler clusters with filler-filler bonds in the unbroken, virgin state. The filler-induced hysteresis is described by an anisotropic free energy density, considering the cyclic breakdown and re-aggregation of the residual fraction of soft filler clusters with already broken, damaged filler-filler bonds. Experimental investigations of the quasi-static stress-strain behaviour of silica and carbon black filled rubbers up to large strain agree well with adaptations found by the developed model. The microscopic material parameters obtained appear reasonable, providing information on the mean size and distribution width of filler clusters, the tensile strength of filler-filler bonds and the polymer network chain density.