The general viscous relation for the response of ice and its implications in the reduced model for ice-sheet flow

Abstract

AbstractAnalyses of confined and unconfined compression combined with shear, and of biaxial stress laterally confined or unconfined, are presented for a general deviatoric viscous relation describing the response of an incompressible material. At present, numerical models for ice-sheet flow commonly adopt a very simple viscous law throughout the ice sheet, in which the deviatoric stress is coaxial with the strain rate, and the single response function depends on only one invariant, and is determined by single stress component tests which cannot verify the validity of the simplification. The analysis presented here is concerned with two-stress-component experimental configurations which could determine the general quadratic form of a viscous relation, with two response functions depending on two invariants. It is shown that the two combined compression and shear tests can also check the consistency of a viscous fluid assumption, but not so the biaxial stress tests. Each test allows a direct assessment of the significance of the quadratic term. It is then shown that a significant quadratic term changes the relative stress magnitudes in the commonly adopted reduced model for ice-sheet flow, and that the crucial simplifications are not achieved.