This thesis considers two subjects concerning constitutive modelling of large-strain behaviour of polymeric materials, namely large-strain elastic deformation of rubbers and large-strain in- elastic deformation of amorphous glassy polymers.

Three-dimensional molecular network theories are studied which use a non-Gaussian sta- tistical mechanics model for the large strain extension of molecules. Invoking an affine defor- mation 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 gov- erned 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 de- scribe the large-strain elastic hehaviour of rubbers. Detailed comparisons with experimental re- sults 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 rub- bers.

Furthermore, the full network model for rubber elasticity is re-formulated in a more effi- cient and more micromechanics motivated manner. Based on such a full network description, a so-called full network model for rubber photoelasticity is proposed, by introducing direction- al polarizabilities into the individual links of the idealized randomly-jointed chain. This optical theory can be used to study the optical properties or birefringence-strain behaviour of rubbers in arbitrary 3-D deformation states. Detailed comparisons with two approximate models, namely the classical three-chain model and a so-called eight-chain model for rubber photoelas- ticity, which is also developed in this thesis, are provided for different types of deformation. The predicted numerical results are compared with experimental data found in the literature.

The network model is further applied to describe the orientation hardening in amorphous glassy polymers caused by stretching of the entanglement network. A 3-D constitutive model is then developed to describe the large strain inelastic deformation behaviour of amorphous glassy polymers, featuring time-, temperature- and pressure-dependent yield, softening and subsequent orientational hardening.

Large-strain elastic-viscoplastic torsion of circular tubes and solid bars of glassy polymers is investigated under fixed-end as well as free-end conditions. The solution of the problem is obtained numerically by means of simple, special purpose finite elements. The differences be- tween free-end and fixed-end torsion are emphasized. Numerical results predicted by the model are compared with experimental results for polycarbonate found in the literature.

Neck propagation, or commonly termed cold drawing, is a standard technique used to ori- ent the molecular chains of the polymers and thereby harden the polymer products. Finite ele- ment analysis is used to numerically simulate plane strain tension, focussing attention on necking and neck propagation. The effects of initial imperfection, strain softening, orientation hardening, strain-rate as well as the geometry and boundary conditions are discussed in detail. The mechanisms of necking and neck propagation are discussed in some detail based on the detailed parameter study.

Similar to the well-known neck- propagation phenomenon, shearing of polymer materials often reveals the initiation and subsequent propagation of a shear band. Finite element analysis is used to numerically simulate large plane strain, simple shear tests, focussing attention on the initiation and propagation of the shear band. The mesh sensitivity and effects of initial imper- fection, strain softening, orientation hardening, strain-rate as well as the edge effects are dis- cussed in detail. It appears that the intrinsic softening is the driving force to promote initiation of the shear band and its propagation in the shear direction, while the orientation hardening is the driving force for widening of the shear band. The predicted numerical results are compared with experimental data for polycarbonate found in the literature.