## Current formalization

Field and laboratory experiments carried out in the 1940s and 1950s led to the initial formulation of a constitutive relation for ice, now known as Glen's flow law (Glen, 1955). In tensor notation with i, j = x, y, z, the three axes of the Cartesian coordinate system, it takes the form eij—Ate 1Tj

where é¡j is the strain rate tensor, A is a rate factor that reflects ice hardness (principally considered as solely temperature-dependent), Te is the effective stress, which is a measure of the total stress state of the ice under consideration, Tj is the imposed stress tensor and the exponent n is generally taken to have a value of ca. 3 (Hooke, 1981). Although ice can be modelled alternatively as a Newtonian viscous fluid (n = 1, whereby strain rate varies linearly with the applied stress) or as a plastic (whereby ice fails completely, giving infinite strain at a given critical stress of ca. 100kPa), Glen's non-linear viscous relation remains the most commonly used representation. Yet, owing to its non-linearity and the fact that the calculated strain rate is not just dependent on the imposed stress but on the total stress state, this equation is a challenge to solve at the ice-mass scale.

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