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.
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BibTeX
@misc{nutte2026finitestrain,
title = {{A finite-strain logarithmic viscoelastic model for Antarctic ice shelves based on an additive split}},
author = {Maxime Nutte and Sebastian Skatulla and Carlo Sansour},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08451},
eprint = {2609.08451},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08451},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A finite-strain logarithmic viscoelastic model for Antarctic ice shelves based on an additive split
AU - Maxime Nutte
AU - Sebastian Skatulla
AU - Carlo Sansour
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08451
UR - https://arxiv.org/abs/2609.08451
AB - 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.
ER -