A uniform stress,multi-grain model for migration recrystallization in polar ice

A multi-grain model for a migration recrystallization process in polar ice is presented. The model is based on the Sachs-Reuss approximation of the stress homogeneity in a polycrystalline aggregate. An individual crystal of ice is treated as a transversely isotropic and incompressible medium which deforms by viscous creep. The highly anisotropic viscous behaviour of the ice crystal is described by a constitutive law expressing microscopic strain-rate in terms of the deviatoric stress and three fluidity parameters that define different viscous resistances of the crystal in different glide directions. It is assumed that the recrystallization occurs in those crystals in the aggregate which are most slowly deforming, and new crystals are nucleated at orientations which favour the crystal deformation by basal glide. The model predictions are illustrated by results of numerical simulations of simple flows, showing the evolution of the microscopic structure of ice and the variation of macroscopic viscosities with increasing deformations.