A model for the tangent viscous behaviour of anisotropic polar ice

During the deformation of polar ice, a fabric develops which results in a macroscopically anisotropic behaviour. Since the plastic anisotropy of the ice single crystal is very high, the effect of a strong (single maximum) fabric on the macroscopic flow law cannot be neglected when simulating the flow of an ice sheet. As this is already a difficult task when using the familiar isotropic power law for ice, the fabric evolution and related macroscopic mechanical behaviour model, to be implemented in such a simulation, must be realistic yet simple enough to achieve results within a reasonable level of complexity, at least as a first step. To this aim, we propose to model polar ice as a transversely isotropic medium; while simplifying the problem, this captures the essential features of the in-situ observed fabrics. The macroscopic mechanical behaviour of the ice polycrystal is obtained by using an orientation distribution function (ODF) for the c axes of the grains, which characterizes the fabric, and a self-consistent scheme, considering each single crystal as transversely isotropic. The evolution of the ODF is described by a conservation equation. In the first stage, this model was run in the simple cases of uniaxial compression and tension along the orthotropy symmetry axis.