Three-dimensional numerical simulations on the hyperelastic behavior of carbon-black particle filled rubbers under moderate finite deformation

Based on the structural characteristics of reinforced elastomer in mesoscopic scale, two schemes of three-dimensional numerical approximation are proposed for simulating the hyperelastic behavior of carbon-black particle filled rubbers under moderate finite deformation, in which the filler particles are respectively assumed as two different shaped polyhedrons and randomly distributed in rubber matrix. With these multi-particulate numerical models, the computational hyperelastic stress–strain relationship for filled rubbers with different reinforcement volume fractions (10–20%) are obtained, which indicate that our new presented models can take into account the effect of filler particles on the overall mechanical behavior of elastomers well up to 20% strain. Based on the simulation results, the strain distribution in matrix part of composite is discussed and analyzed in detail at different overall stretch levels, which approximately obeys the statistical Gaussian distribution.