Strain-rate formulation of ice fabric evolution

Reorientation of individual crystal-glide planes as isotropic surface ice is deformed during its passage to depth in an ice sheet, lattice rotation, creates a fabric and associated anisotropy. A simple macroscopic description is that these material glide planes are rotated towards planes normal to an axis of compression, and away from planes normal to an axis of extension, inducing an instantaneous orthotropic viscous response with reflexional symmetries in the planes orthogonal to the current principal stretch axes. An orthotropic viscous law is presented for the strain rate expressed in terms of the deviatoric stress, the deformation, and three structure tensors based on the principal stretch axes. This anisotropic relation is expressed in terms of a single fabric response function in addition to the isotropic ice viscosity. The predicted responses in uniaxial compression and simple shear are determined. While the uniaxial response yields an explicit relation between the axial strain rate and stress, it is found that the shear response is governed by three, complicated, coupled relations between the shear strain rate and three deviatoricstress components. The new result derived here is the solution of this system: an explicit relation between the shear strain rate and shear stress. Correlation of these relations with idealized uniaxial and shear responses is then used to determine the required fabric function in the model law.