Prediction on mechanical behavior of carbon black filled rubber composites based on periodic boundary conditions

Based on the relation of macroscopic and microscopic characteristics of carbon black filled rubber composites, representative volume element with random distribution pattern has been proposed, the boundary conditions for the periodic microstructures has been discussed, and three dimensional multi-particles RVE numerical model has been established to study and analyze the macro mechanical properties of the carbon black filled rubber composites by the micromechanical finite element method. The research shows that the compatibility of the deformation field and stress field in macrostructure are ensured by the periodic boundary conditions, the modulus of the rubber composite is increased considerably with the introduction of carbon black filler particles, and the effective elastic modulus of the rubber composite is increased with the increase of the carbon black particle volume fraction. In the simultaneous, the results of the prediction on the effective elastic modulus of the rubber composite made with this numerical model are consistent with the experimental results, and better than the predictions of the model proposed by Bergstrom, which demonstrate that this model can be used for simulation analysis of effective properties of the carbon black filler particle reinforced rubber matrix composites.