ABSTRACT
This chapter describes micromechanically based constitutive models for a single chain and defines the macroscopic stress response of the polymer network by a directly evaluated micro–macro transition in a discrete orientationspace defined on a micro–sphere. It presents a new micromechanically based constitutive approach that accounts for elasticity combined with the deformation–induced anisotropic damage in rubbery polymers. A continuum formulation is constructed by a superimposed modeling of a crosslink–to–crosslink (CC) and a particle–to–particle (PP) network. The former is described by the non–affine elastic network model proposed by Miehe et al. The Mullins–type damage phenomenon is embedded in the PP network and micromechanically motivated by a breakdown of bonds between chains and filler particles. The anisotropic damage phenomenon is embedded into the PP network. The CC network part t¯cc is assumed to be isotropic, whereas the PP network part t¯pp provides a deformation–induced anisotropy that is described by the temporal evolution of the damage variables.
