Constitutive laws for ice

A theoretical discussion of models which describe the transient and secondary creep response of polycrystalline ice is presented, including a hypothesis which incorporates temperature dependence in the rate laws by the introduction of a reduced time scale. The secondary response is described by a general non-linear incompressible viscous fluid law, and it is shown that bi-axial stress experiments are insufficient but combined shear and compression experiments are sufficient to determine, in principle, the general response functions. Transient creep can be described qualitatively by a viscoelastic fluid model, and the most simple material memory influence is given by dependence on the current creep acceleration which leads to a first order differential relation between stress and strain rate. The secondary creep response is incorporated as a steady asymptotic limit with the time scale of significant transient creep governed by the response coefficients. Quantitative tests of such transient response require data from experiments at short time intervals, and in particular the determination of an initial strain rate to complement the differential law.