Microstructure-based modelling of arbitrary deformation histories of filler-reinforced elastomers

A physically motivated theory of rubber reinforcement based on filler cluster mechanics is presented considering the mechanical behaviour of quasi-statically loaded elastomeric materials subjected to arbitrary deformation histories. This represents an extension of a previously introduced model describing filler induced stress softening and hysteresis of highly strained elastomers. These effects are referred to the hydrodynamic reinforcement of rubber elasticity due to strain amplification by stiff filler clusters and cyclic breakdown and re-aggregation (healing) of softer, already damaged filler clusters. The theory is first developed for the special case of outer stress–strain cycles with successively increasing maximum strain. In this more simple case, all soft clusters are broken at the turning points of the cycle and the mechanical energy stored in the strained clusters is completely dissipated, i.e. only irreversible stress contributions result. Nevertheless, the description of outer cycles involves already all material parameters of the theory and hence they can be used for a fitting procedure. In the general case of an arbitrary deformation history, the cluster mechanics of the material is complicated due to the fact that not all soft clusters are broken at the turning points of a cycle. For that reason additional reversible stress contributions considering the relaxation of clusters upon retraction have to be taken into account for the description of inner cycles. A special recursive algorithm is developed constituting a frame of the mechanical response of encapsulated inner cycles. Simulation and measurement are found to be in fair agreement for CB and silica filled SBR/BR and EPDM samples, loaded in compression and tension along various deformation histories.