On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers

Three-dimensional molecular network theories are studied which use a non-Gaussian statistical mechanics model for the large strain extension of molecules. Invoking an affine deformation assumption, the evolution of the network — consisting of a large number of molecular chains per unit volume, which are initially randomly oriented in space — is shown to be governed by a balance equation in orientation space. Eulerian and Lagrangian type formulations of these balance equations are given, and the closed-form analytical solution for the so-called Chain Orientation Distribution Function is derived. This full network model is then used to describe the large strain inelastic behaviour of rubber-like materials. Detailed comparisons with experimental results and with two approximate models, namely the classical three-chain model and a very recently proposed eight-chain model, are provided for different types of deformation and rubbers. Finally, the network model is applied to describe the orientational hardening in amorphous glassy polymers, and confronted with experimental data for polycarbonate. The inherent physical limitations of the network theory for both applications are discussed.