Analytical derivations for the behavior and fabric evolution of a linear orthotropic ice polycrystal

The fabric of polar ice exhibiting orthotropic symmetry (i.e., threeplanes of reflexional symmetry) is described by a, continuous orientation distribution function (ODF) which represents the density of grains whose c axes have a given orientation. For a given ODF, the constitutive law of such anisotropic ice is obtained by a homogenization procedure based on the assumptions that; the ice single crystal behaves as a linear transversely isotropic material and that the grains experience a uniform state of stress. Under loading conditions which respect the symmetries of orthotropy, the evolution of the macroscopic behavior of a polycrystal of ice, as well as the evolution of its fabric, are fully determined by analytical expressions. The solution for a transversely isotropic polycrystal is deduced as a reduction from the orthotropic case. In this special configuration, the results from the present model are compared to fabric measurements made by Thorsteinsson et al. [1997] on the GRIP ice core.