A MICRO-MECHANICALLY BASED CONTINUUM DAMAGE MODEL FOR CARBON BLACK-FILLED RUBBERS INCORPORATING MULLINS EFFECT

THE PROBLEM of Mullins' effect in carbon black-filled rubbers is treated from a micro-mechanical viewpoint and a complete continuum constitutive model is developed. To begin with, a first-order accurate free energy function is derived for the composite in terms of the free energy densities of the constitutents. Second, an exact relation between averaged macroscopic nonlinear strain measures and averaged nonlinear matrix material strain measures is derived under the assumption of affinely rotating particles and a C-degrees continuous motion. Third, the notion of strain-induced matrix-particle debonding is incorporated into the free energy density for the material by exploiting ideas from statistical mechanics. The accuracy of the resulting constitutive model is then demonstrated via comparisons to published experimental data.