Modeling the Mullins effect of rubber-like materials

In this paper, the Mullins effect that is a stress-softening phenomenon of rubber-like materials during cyclic loadings is studied, by considering the energy dissipation process of weak physical and chemical bond rupture. The eight-chain model is used to construct the Helmholtz free energy, with two network structure parameters (the chain density n and the average number of monomer segments of a polymer chain N) being taken as internal variables, which can be derived in terms of a given stretch at the start point of each unloading by analyzing the stored Helmholtz free energy and the unloading stress–stretch relation. Furthermore, a novel method is developed to determine the evolution equations of these internal variables through the analysis of mass conservation and energy dissipation, and then the Mullins effect of rubber-like materials can be theoretically predicted and agree with experimental results, not only for the unloading curves, but also for the first loading curve.