基于加性分解的南极冰架有限应变对数粘弹性模型

中文摘要 AI 辅助

冰架主要通过崩解损失质量，这一过程受近前沿应力场控制，其时间尺度跨越弹性弯曲和粘性蠕变。我们在对数应变空间中为冰川冰构建了一个有限应变麦克斯韦模型。固定参考构型的亨基应变在速率层面加性分解为弹性部分和粘性部分；弹簧为各向同性亨基弹性，阻尼器为基于对数应变率及其功共轭应力的格伦型幂律。在无穷小应变下，阻尼器与格伦流动律一致；本文冰架构型中的弹性应变保持在该范围内。该模型采用中点评估和试对偶的向后欧拉校正进行积分，并在有限元框架中实现。在粘弹性柱基准测试之后，该公式被应用于一个理想化的冰舌，包括随深度变化的密度和模量、随温度变化的流动性，以及具有前缘脚部或基底掏蚀的悬崖几何形状。所得应力场展示了粘弹性和前沿形态如何控制末端附近的张力。

英文摘要

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.

发表机构

• University of Cape Town（开普敦大学）
• Bethlehem University（伯利恒大学）

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