A quadratic viscous fluid law for ice deduced from Steinemann's uni-axial compression and torsion experiments

• Published in: Journal of Glaciology
• Main Authors: R. Staroszczyk, L. W. Morland
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press 2022
• Subjects: Constitutive law; isotropic response; polar ice; viscous creep; Environmental sciences; GE1-350; Meteorology. Climatology; QC851-999; Ice Sheet; Journal of Glaciology
• Online Access: https://doi.org/10.1017/jog.2021.113; https://doaj.org/article/f0f7880f2e3f4f69abe994357796f294

The response of ice to applied stress on ice-sheet flow timescales is commonly described by a non-linear incompressible viscous fluid, for which the deviatoric stress has a quadratic relation in the strain rate with two response coefficient functions depending on two principal strain-rate invariants I2 and I3. Commonly, a coaxial (linear) relation between the deviatoric stress and strain rate, with dependence on one strain-rate invariant I2 in a stress formulation, equivalently dependence on one deviatoric stress invariant in a strain-rate formulation, is adopted. Glen's uni-axial stress experiments determined such a coaxial law for a strain-rate formulation. The criterion for both uni-axial and shear data to determine the same relation is determined. Here, we apply Steinemann's uni-axial stress and torsion data to determine the two stress response coefficients in a quadratic relation with dependence on a single invariant I2. There is a non-negligible quadratic term for some ranges of I2; that is, a coaxial relation with dependence on one invariant is not valid. The data does not, however, rule out a coaxial relation with dependence on two invariants.