A uniform strain, discrete-grain model for evolving anisotropy of polycrystalline ice

Abstract

A discrete-grain model accounting for the induced anisotropy of polycrystalline ice is formulated. An individual ice crystal is supposed to be a transversely isotropic medium whose behaviour is linearly viscous. For such a crystal a frame-indifferent constitutive law involving three microscopic rheological parameters is derived. Assuming that each crystal undergoes a homogeneous deformation of the polycrystalline aggregate (the Taylor approximation), the macroscopic viscous behaviour of the material is determined. The considerations are illustrated by the results of numerical simulations of simple flows, showing the evolution of the oriented structure of the material and the variation of macroscopic viscosities with increasing strains. In addition, the influence of the parameters describing the single crystal anisotropy on the overall behaviour of the aggregate is investigated.