Constitutive Equations for the Back Stress in Amorphous Glassy Polymers

Constitutive equations for the back stress in amorphous glassy polymers based on extended forms of the non-Gaussian James—Guth 3-chain and Arruda—Boyce 8-chain models of rubber elasticity are derived from the extended Wu and van der Giessen non-Gaussian full-network model. A simple and invariant constitutive equation for the back stress tensor is then derived from the Wu and van der Giessen model by an average-stretch approximation. Although the average-stretch model of the full-network amorphous microstructure is more general than other chain cell models, the constitutive equation is the same as the 8-chain back stress relation. Back stress equations for a class of extended phenomenological models, including the Gent material model, are described.