Two orthotropic models for strain-induced anisotropy of polar ice

As polar ice descends from the free surface to depth in a large ice sheet, it undergoes deformations which give rise to the formation and subsequent evolution of a fabric and associated anisotropy. In this paper two orthotropic models of such strain-induced anisotropy are considered. Model A is based on analysis of the microscopic behaviour of an individual ice crystal with transversely isotropic response and assumed uniform stress in a polycrystal. The macroscopic response of the ice aggregate is then derived by applying the concept of an orientation distribution function, and the resulting viscous law relates the strain rate to the stress and three structure tensors. In model B it is assumed that the macroscopic response of ice is determined by the fabric induced entirely by macroscopic deformations, and all microprocesses taking place at the grain level are ignored. A constitutive relation is derived from a general frame-indifferent law for orthotropic materials, and expresses the stress in terms of the strain rate, strain and three structure tensors. The two models are applied to determine the viscous response of ice to continued uniaxial compression and simple shearing in order to compare the predictions of both theories.