A finite-strain logarithmic viscoelastic model for Antarctic ice shelves based on an additive split

Abstract

Ice shelves lose mass primarily by calving, a process controlled by the near-front stress field on timescales that span elastic flexure and viscous creep. We formulate a finite-strain Maxwell model for glacier ice in logarithmic strain space. The Hencky strain of a fixed reference configuration is split additively at the level of rates into elastic and viscous parts; the spring is isotropic Hencky elasticity and the dashpot is a Glen-type power law written on the logarithmic strain rate and its work-conjugate stress. At infinitesimal strain the dashpot coincides with Glen's flow law; the elastic strains in the ice-shelf configurations of this paper remain in that regime. The model is integrated with a midpoint evaluation and a backward-Euler correction of the trial dual, and implemented in a finite-element setting. After a viscoelastic column benchmark, the formulation is applied to an idealised ice tongue, including depth-dependent density and moduli, temperature-dependent fluidity, and cliff geometries with a frontal foot or basal undercutting. The resulting stress fields show how viscoelasticity and front morphology control tension near the terminus.