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A material model for the simulation of anisotropic behaviour due to texture development in polar ice is presented. Emphasis is laid on the strain-induced texture development and its relaxation due to rotation recrystallization and grain boundary migration in the low-velocity regime. The model is based on two scales (mesoscopic approach). Kinematics, balance equations and constitutive assumptions are defined with respect to the grain level (mesoscale). Slip-system behaviour is assumed to be Newtonian. Recrystallization and grain boundary migration are taken into account via a diffusion-type evolution of the crystallites orientation. Due to the inextensibility of the ice crystallites along their c axes, the Sachs–Reuss assumption is adopted. Volume averaging yields associated macroscopic relations, where the internal structure is represented by a second-order structure tensor. The proposed approach is illustrated by applying it to initially isotropic material under homogeneous deformation, giving results qualitatively in agreement with experimental evidence. Finally, it is shown that the proposed model is, under some simplifying conditions, directly related to phenomenological internal variable models (e.g. Morland and Staroszczyk, 1998).

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.

[1] A model for simulations of the ice microstructure evolution during its deformation is presented. Several competing processes are considered which lead to the development of anisotropic crystal c axes orientation distribution. Existing theories of the plastic deformation and recrystallization dynamics are combined in a discrete algorithm based on the cellular automata approach. We simulate the evolution of the fabric and texture, that is, orientations and sizes of single crystals of polycrystalline ice which experiences uniaxial compression, the loading condition close to that at the summit of the Greenland Ice Sheet. The results of our simulations are in a good qualitative agreement with the data obtained from the Greenland Ice Core Project ice core drilled at this location.

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