A micromechanics-based incremental damage model for carbon black filled rubbers

This paper is to develop a simple micromechanics-based model taking account of progressive damaging for carbon black (CB) filled rubbers. The present model constitutes of the instantaneous Young's modulus and Poisson's ratio characterizing rubber-like material, a double-inclusion (DI) configuration considering the absorption of rubber chains onto CB particles, and the incremental Mori-Tanaka formula to compute the effective stress–strain relations. The progressive damage in filled rubbers is described by the DI cracking, which is represented by the remaining load–carrying capacity. The present predictions are capable of embodying the well-known S-shaped response of filled rubbers, and also verified by the comparison with the experimental and analytical results. Moreover, strain localization effect is clearly demonstrated by finite element method (FEM) simulations, and reaches a decisive interpretation to the complicated synergic micro-mechanisms between hard fillers and soft phase in such flexible composites.