Microstructure‐based modelling and FE implementation of filler‐induced stress softening and hysteresis of reinforced rubbers

Source abstract

Abstract Reinforcement of rubber by nanoscopic fillers induces strong nonlinear mechanical effects such as stress softening and hysteresis. The proposed model aims to describe these effects on a micromechanical level in order to predict the stress‐strain behaviour of a rubber compound. The material parameters can be obtained by fitting stress‐strain tests. These quantities have a clear defined physical meaning. The previously introduced “dynamic flocculation model” was extended for general deformation histories. Stress softening is modelled by hydrodynamic reinforcement of rubber elasticity due to strain amplification by stiff filler clusters. Under stress these clusters can break and become softer, leading to a decreasing strain amplification factor. Hysteresis is attributed to cyclic breakdown and re‐aggregation of damaged clusters. When stress‐strain cycles are not closed, not all of these clusters are broken at the turning points. For the resulting “inner cycles” additional elastic stress contributions of clusters are taken into account. The uniaxial model has been generalized for three‐dimensional stress states using the concept of representative directions. The resulting 3D‐model was implemented into a Finite Element code, and an example simulation is shown. Good agreement between measurement and simulation is obtained for uniaxial inner cycles, while the 3D‐generalization simulates the behaviour closer to the experiment than the original model.