On the role of grain growth, recrystallization and polygonization in a continuum theory for anisotropic ice sheets

We outline how to incorporate microscale effects of polycrystalline ice into a continuum description. Actually, analyses of ice cores in Antarctica show that different microstructures generally produce different responses, i.e. a non-uniform distribution of c axes gives rise to anisotropic behaviour. It has been recognized that, to describe certain microstructural processes, like recrystallization or polygonization, we need a parameter able to switch them on (e.g. dislocation density or its associated lattice distortion energy). With this in mind, balance equations for a continuum theory of an anisotropic ice sheet undergoing recrystallization have been recently proposed. In this work, we examine relations for some constitutive quantities, in order to take into account the effects of grain-boundary migration, nucleation and polygonization. We check our assumptions by explicit comparison with the first 1200 m of the Byrd (Antarctica) ice core. Current literature usually gives a relation between normal grain growth and grain boundary migration rate. Here, an equation for normal grain growth which also incorporates the influence of polygonization is suggested. It is based on experimental data from the same core in Antarctica. Polygonization is a microscopic process, but here we present a continuum description of the bending stresses which promote the fragmentation of crystallites in terms of the theory of mixtures with continuous diversity.