Comparison of finite-element and homogenization methods for modelling the viscoplastic behaviour of a S2-columnar-ice polycrystal

Abstract

The main homogenization schemes used to model the behaviour of polycrystalline ice are assessed by studying the particular case of a two-dimensional polycrystal which represents natural S2-columnar ice. The results of the uniform-stress, uniform-strain-rate and one-site self-consistent models are compared to finite-element computations. The comparisons were made using the same model of grain, described as a continuous transversely isotropic medium, in the linear and non-linear cases. The uniform-stress and uniform-strain-rate models provide upper and lower bounds for the macroscopic fluidity which are too far from each other to be useful when a degree of anisotropy relevant to ice is considered. Although the self-consistent model gives a weak representation of the interaction between a grain and its surroundings, due to the strong anisotropy of the ice crystal, the resulting macroscopic behaviour is found to be acceptable when compared to the results from finite-element computations.