An analytical approach to deformation of anisotropic ice-crystal aggregates

Abstract

Deformation rates of single hexagonal crystals, deforming by glide on the basal plane, are described as a function of stress state and crystal orientation. These results are used to infer the deformation rate of crystal aggregates assuming that the stress distribution within the crystal aggregate is homogeneous. Analytical equations for the deformation rate of anisotropic ice aggregates are derived for vertically symmetric girdle fabric. This type of fabric is approximated by a uniform distribution of c-axis orientations between a cone angle and a smaller girdle angle relative to the symmetry axis. For simple shear stress acting on a single-maximum fabric there is a slight de-enhancement for cone angles of 60–90°. In uniaxial compression a maximum enhancement of ∼1.7 occurs at a cone angle of 57°. A pure shear stress state has similar features, with the additional complication that it causes a non-zero transverse strain rate, except for perfect vertical alignment of crystals and isotropic fabric. In combined states of stress the contribution of each stress component to the strain rate depends on fabric. A single enhancement factor is not adequate to describe the effects of anisotropy for complex stress states.

The role of crystal fabric in flow near an ice divide

“…Azuma, 1994;Castelnau and others, 1996;Godert and Hutter, 1998;Gagliardini and Meyssonnier, 1999;Thorsteinsson, 2001Thorsteinsson, , 2002. Their approaches differ primarily in how they relate the stress applied to the ice aggregate to the local deformation rate of a crystal within the aggregate.…”

“…We take the next step by combining an analytical description of deformation of a polycrystal with a vertically oriented crystal fabric together with a non-linear constitutive relation for bulk flow of ice. The analytical description is a linear version of the flow law derived by Thorsteinsson (2001). The benefit of this analytical description is its ability to capture the impact of crystal fabric on deformation near a divide, yet it is simple to implement in ice-sheet models.…”

Fabric development with nearest‐neighbor interaction and dynamic recrystallization

“…This also allows us to update the orientation of the three Burgers vectors in the basal plane [Thorsteinsson, 2001].…”

“…Then the mean and standard deviation (SD) of the strain rates are calculated for the 100 numerical experiments. Since the correct strain rate for an infinite number of crystals is known analytically [Thorsteinsson, 2001], it can be used to normalize the resulting strain rates. Figure 9 shows how the number of crystals used in a calculation affects the accuracy.…”

“…The fabric development is qualitatively known from thin section and sonic logging measurements. The c axes rotate toward the compression axis [van der Veen and Whillans, 1994;Morland and Staroszczyk, 1998;Gödert and Hutter, 1998;Thorsteinsson, 2001].…”