Material update procedure for planar transient flow of ice with evolving anisotropy

A flow law for polar ice is derived, which takes into account the effect of deformation-induced anisotropy due to hexagonal single-crystal symmetry. Attention is focused on the main effect of crystal-lattice rotation. Existence of a continuous so-called orientation-distribution function ODF, for the crystals is assumed. With its help the microscale constitutive behaviour is transformed to the large-scale. This transformation is simplified by imposing different consistency conditions (CC) due to Voigt-Taylor (VT) and Sachs-Reuss(SR), respectively. Here we take the grain interaction into account by linearly combining the VTand the SR conditions, i.e. by one additional parameter determining the relative weight of the two. A coupled finite-element-finite-volume approach is used to account for fabric evolution at the ice-sheet scale. For different CC, VT and SR, an orientation update is derived for planar flow, which results in only three additional degrees of freedom at each finite-element integration point to account for orthotropic material symmetry. Computations for the GRIP-core data demonstrate that a better fit can be obtained than with VT or SR alone.