Analysis of Calving Events in Antarctic Ice Shelves Using Configurational Forces

Abstract

Previous studies on the sensitivity of cracks in ice shelves with different boundary conditions, stress states and density profiles revealed the need for further analyses. As the transfer of boundary conditions from dynamic ice flow simulations to the linear elastic fracture analyses proved to be a critical point in previous studies, a new approach to relate viscous and elastic material behaviour is proposed. The numerical simulations are conducted using Finite Elements utilizing the concept of configurational forces. To show the applicability of the approach, a 2-dimensional plane stress geometry with volume loads due to the ice shelf flow is analyzed. The resulting crack path is compared to available crack paths from satellite images. In a first approach, ice can be regarded as a visco-elastic material represented by a Maxwell element that consists of a linear elastic spring and a nonlinear dashpot. For this material the stress can be written as σ v = σ e = σ with the elastic stress σ e and the viscous stress σ v . Under steady state conditions and the absence of volume forces, the equilibrium condition yields(1)For a given horizontal ice flow field with the velocities v(x, y) in the plane of the shelf, the viscous surface stress σ v can be evaluated using Glen's flow law [1] yielding, σ v = Bd 1−n n (trD1 + D), with the effective strain rate d = 1 2 tr(D 2 ), the strain rate tensor D and the material parameters B ≈ 7 · 10 7 Pa s 1 3 and n = 3. If we now understand the divergence of the viscous surface stress as a negative viscous volume force f v = − div σ v , Eqn. (1) can be rewritten asInstead of using stress or equivalent displacement boundary conditions, which are difficult to determine, the ice shelf is loaded by viscous volume forces yielding a stress field in the unfractured ice shelf that represents the viscous stresses.

Ice shelf rift propagation: stability, three dimensional effects, and the role of marginal weakening

“…This contact is expected to occur at the top of the ice shelf and in the region near the rift tip, as illustrated in Fig. 1b (Plate et al, 2012;Levermann et al, 2012;Borstad et al, 2017) and near-tip deformation (Larour et al, 2004a, b).…”