Computational aspects of localized deformations in amorphous glassy polymers

Amorphous glassy polymers are prone to strain localization due to the particular constitutive behaviour of these materials where yield is followed immediately by intrinsic strain softening and where increasing strain hardening occurs at continued deformation. With a view on the reliable analysis of localization phenomena, this paper presents a so-called rate tangent formulation of a recently proposed constitutive model for the rate-dependent, large strain behaviour of glassy polymers. As part of the derivation, rate forms are presented for non-Gaussian three-chain, eight-chain and full network models for rubber elasticity. The implementation in viscoplastic-type finite element formulations is discussed, and is used, as an example, to study shear localization in glassy polymers under plane strain or axisymmetric compression. Computations with different material parameters confirm existing experimental observations that localization can take place in relatively diffuse (widening) shear bands or in families of relatively fine (multiplying) shear bands.