Structural-phenomenological simulation of the mechanical behavior of rubbers

It is hypothesized that, during deformation of rubbers, polymer chains slip off the layers at filler particles into voids between inclusions and high-strength polymer fibers in the uniaxially oriented state are formed in the voids. As a result, the macroscopic strength of elastomers increases by an order of magnitude and the elongation at break simultaneously increases relative to the unfilled elastomer. Aggregates of carbon black particles that occur close to one another in the initial sample depart to very large distances upon stretching the material. The fibers that tie the aggregates must extend their length by a factor of a few tens in this case. A mathematical model that takes into account these processes is proposed. It was shown that the set of constitutive equations makes it possible to simulate with good accuracy both the viscoelastic behavior of rubbers and the Mullins softening effect under finite strain conditions.