A network evolution model for the anisotropic Mullins effect in carbon black filled rubbers

To the best of our knowledge, there are no constitutive models that properly describe experimental data on anisotropy of the Mullins effect. In this paper, such a micro-mechanical model is proposed for carbon black filled rubbers. The model describes the deformation induced anisotropy and permanent set as well. Damage of the polymer-filler network is considered as a consequence of chain sliding on or debonding from aggregates. In contrast to previous works on anisotropy of the Mullins effect we do not introduce any phenomenological damage function. Damage in different directions is governed by a network evolution concept which describes the changes in the inter-aggregate distribution of polymer chains. The model includes a few number of physically motivated material constants and demonstrates good agreement with own experimental data on subsequent uniaxial tensions in two orthogonal directions.