A structure-based constitutive equation for filler-reinforced rubber-like networks and for the description of the Mullins effect

A constitutive equation for elastomeric networks (ABGIL) was proposed by us previously and tested with a good success (Polymer 2003, 2004). It incorporates the Arruda and Boyce connectivity term based on Langevin statistics, the constraint term based on a generalized formulation of different tube theories and a semi-empirical concept of a strain-dependent finite extensibility parameter. The ABGIL equation has now been extended for filler-reinforced networks (ABGILFIL equation) by incorporating the concept of Klüppel et al. of a strain-amplification function describing the strain-induced filler-cluster breakdown. The proposed ABGILFIL equation is shown to offer a very good description of stress–strain dependences in different deformation modes of virgin and strain-softened networks of natural rubber and SBR, up to high strains. From the knowledge of the first-extension behavior, the Mullins-type strain-softening is predicted and shown to be composed of two contributions: the strain-induced filler-cluster breakdown and the strain-induced increase in the network mesh size, which is consistent with the mechanism of entanglements removal at the matrix–filler interface recently proposed and discussed by Hanson et al.