A general continuum damage model for soft composites

Soft composites, including filled rubbers, nanocomposite gels, double network hydrogels, and multiple network elastomers, all exhibit stress-softening behavior in loading-unloading cycles, also denoted as the Mullins effect. Though qualitatively this damage behavior shows similar features, the details still vary with material types. In this work, we provide a general approach towards modeling the Mullins effect for soft composites based on continuum damage mechanics. We start with formulating a one-dimensional damage model. A logarithmic damage variable is employed, while a damage potential function is adopted to obtain the evolution law for the damage variable. We then extend the one-dimensional damage model to three-dimensions. The eight-chain type micro-macro transition is used to formulate an isotropic damage model. An anisotropic damage model is constructed based on the full network model, while a new micro-macro mapping is used to determine the micro stretch from the macro deformation. With this new mapping, the full network model appears in a consistent format in that the free energy, dissipation, and stress are respectively given by the average of their directional micro counterparts. In the current approach, two constitutive functions need to be determined: the elastic free energy density and the stored energy limit. Simple forms of these two constitutive functions are provided with only a small set of model parameters. The resulting models are then successfully applied to describe the stress response in loading-unloading cycles and the anisotropic response of predeformed materials for different kinds of soft composites.