Flow-induced anisotropy in polar ice and related ice-sheet flow modelling

As fibers or other crystalline materials exhibiting hexagonal symmetry, the crystal of ice can be orientated by using only one single vector, i.e. its c-axis. Such a characteristic allows to apply specific methods to deal with the properties of the polycrystalline aggregate. Among others, the fabric (texture) of the ice polycrystal can be described by an ODF, i.e. a scalar function of two angles that gives the distribution of the orientation of all the constituents (grains).This paper presents a strain-induced anisotropic flow law for polycrystalline ice and the associated equations describing the evolution of its fabric. This constitutive law is formulated at the polycrystal scale and tabulated using a micro–macro model. The fabric is defined by the second- and fourth-order orientation tensors for the c-axes, assuming the so-called “invariant-based optimal fitting closure approximation”. Both the anisotropic constitutive law and the fabric evolution equations have been implemented in a finite element code in order to solve large scale ice flow problem. As an application, the flow of an idealized ice sheet over a bumpy bed is studied.