Modelling discontinuities in ice flow using the Material Point Method and elastoplasticity

Understanding glaciers evolution is of major concern to evaluate their contribution to sea level rise in the context of global warming. Among the various processes involved in glacier dynamics, fractures like the calving of ice at the front of marine terminating glacier and crevasse formation affect the stress state, potentially modifying the glacier’s velocity. Crevasses also impact the melting rate. The fractures alter the roughness of the ground, increasing the amount of absorbed radiation, and open new networks in which the meltwater is likely to penetrate deeper toward the glacier bed.

In this work we propose to model fractures in glacier based on finite strain elastoplasticity, using the Material Point Method (Wolper et al. 2021): we solve the classical governing equations for ice deformation in an Eulerian-Lagrangian framework and we use a strain softening Drucker-Prager constitutive model to simulate plasticity. Thanks to the Lagrangian part of the model, the fractures appear explicitly where high levels of total plastic deformation are reached. The behaviour of a glacier flowing over a step in the bedrock is investigated. The simulations show that crevasse patterns appear with regular spacing between the fractures. We perform a parametric study to determine which parameters affect the length of these patterns and potential dimensionless numbers are outlined.