A model for the tangent viscous behaviour of anisotropic polar ice

Abstract

During the deformation of polar ice, a fabric develops which results in a macroscopically anisotropic behaviour. Since the plastic anisotropy of the ice single crystal is very high, the effect of a strong (single maximum) fabric on the macroscopic flow law cannot be neglected when simulating the flow of an ice sheet. As this is already a difficult task when using the familiar isotropic power law for ice, the fabric evolution and related macroscopic mechanical behaviour model, to be implemented in such a simulation, must be realistic yet simple enough to achieve results within a reasonable level of complexity, at least as a first step.To this aim, we propose to model polar ice as a transversely isotropic medium; while simplifying the problem, this captures the essential features of the in-situ observed fabrics. The macroscopic mechanical behaviour of the ice polycrystal is obtained by using an orientation distribution function (ODF) for the c axes of the grains, which characterizes the fabric, and a self-consistent scheme, considering each single crystal as transversely isotropic. The evolution of the ODF is described by a conservation equation. In the first stage, this model was run in the simple cases of uniaxial compression and tension along the orthotropy symmetry axis.

A user-friendly anisotropic flow law for ice-sheet modeling

“…As an example, the expected experimental value of 10 is obtained for ¼ 0:04 and ¼ 1 (Meyssonnier and Philip, 1996).…”

“…As shown in Figure 3, " 0 = depends strongly on , whereas has only a small influence. With a self-consistent model based on a continuum description of the fabric and on grain constitutive law (25), Meyssonnier and Philip (1996) derived the following relation when ¼ 1:…”

Change in ice rheology during climate variations – implications for ice flow modelling and dating of the EPICA Dome C core

“…The six dimensionless viscositiesη i (i=1, 2, ..., 6) are tabulated as a function of the two independent eigenvalues of the second order orientation tensor using a self-consistent model (Castelnau et al, 1996a;Meyssonnier and Philip, 1996). The linear grain behaviour is such that a grain deforms 25 times faster by shear parallel to basal plane compared to shear orthogonal to the basal plane.…”

Two orthotropic models for strain-induced anisotropy of polar ice

“…Foll owin g M eyssonnier a nd Philip (1996), the rotation m atrix R that defin es the orientation of the g rain in {R} is governed by th e relation wher e R T is the transp ose of R , th e superposed dot denotes the time d eri vative, W g a nd W a re spins (rates of rotation )…”

“…Assuming transve rse isotropy for each individual crystal a nd a linea r res ponse to de\·iatori c stresses, th e macroscopic stra in rate of the aggregate is deri\·ed by a pplying the ODF concept. Compared to Meyssonni er a nd Philip (1996), Svendse n and Huller (1996) and Godert a nd Hutter (1998), additi onal parameters a rc introduced into the ODF. Owing to th e extra parameters, the deri\·ati on of a macroscopica lly orthotropic (instead of transversely iso tropic ) viscous law relating th e strain rate to the deviatori c stress a nd three structure tensors is poss ibl e.…”