Micro-Structure Based Modeling of Elastomer Materials

A micro-mechanical model of hyperelasticity and stress softening of filler reinforced elastomer materials is presented. It is based on recent investigations of filler morphology in elastomers and considers an advanced concept of rubber elasticity of bulk polymer networks together with a micromechanical model of stress induced filler cluster breakdown. The polymer network is described by a non-affine tube model of rubber elasticity with highly entangled chains, which takes into account that fluctuations in bulk networks are strongly suppressed by packing effects. The evaluation of stress softening is obtained via a pre-strain dependent hydrodynamic amplification of the rubber matrix by a fraction of rigid filler clusters with virgin filler-filler bonds. The filler-induced hysteresis is described by a cyclic breakdown and re-aggregation of the residual fraction of more soft filler clusters with already broken filler-filler bonds.

From the simulations of stress-strain cycles at small and medium strain it can be concluded that the model of cluster breakdown and re-aggregation for pre-strained samples represents a fundamental micro-mechanical basis for the description of non-linear viscoelasticity of filler reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of the polymer network as well as the elasticity and fracture properties of flexible filler clusters.

It is shown that the developed concept is in fair agreement with experimental stress-strain data of carbon black and silica filled elastomers. The obtained microscopic material parameter 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. In particular it is shown that the model fulfils a “plausibility criterion” important for FEM applications. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily.