This paper presents a formulation of a continuum model for so-called (stress or deformation) induced anisotropy in natural ice which, unlike computer-based Taylor-type models, can be incorporated in numerical simulations of large ice masses to account for the effects of this process on the flow of these bodies in a physical fashion. To do this, we treat natural ice as a rigid-elastic, non-linear inelastic material which can develop transverse isotropic behaviour (accounting for the simplest kind of induced anisotropy in natural ice masses), where the degree of such anisotropy at each point is controlled by the distribution of crystal glide-plane orientations there. This distribution is described by a so-called orientation-distribution function, for which an evolution relation can be derived. The central constitutive assumption of this formulation relates this distribution to the “structure” tensor representing the transverse isotropy of the material. On the basis of this relation, the model predicts in particular isotropic (e.g. classical Glen’s flow-law type) behaviour at a given point when the distribution of crystal glide-plane orientations is uniform there.
A continuum approach for modelling induced anisotropy in glaciers and ice sheets