A phase-field description of crevasse growth: comparison of elastic, Maxwell, and Kelvin-Voigt models for ice

Uncertainty in the rate and extent of ice lost from Antarctica and Greenland is the largest source of uncertainty in predicting global sea-level rise, largely due to a poor understanding of the mechanisms governing iceberg calving. Ice-shelf fracture models are typically estimated using a linear elastic model for ice. However, ice exhibits both elastic and viscous behavior in response to a load. This is evidenced by the observation that fractures within glaciers reduce their ability to support a load, resulting in accelerated ice flow downstream. 

To examine the coupling between the flow response of ice and crevasse growth, we use a phase-field description of ice fracture to compare crevasse propagation rates. We examine fracture rates amongst a linearly elastic, Maxwell, and Kelvin-Voigt model of ice during deformation. We impose Robin boundary conditions for a fixed ice-shelf with constant rates of strain downstream and further compare two domains, in which the ice-shelf is either being longitudinally stretched from upstream flow or vertically bent due to tidal forcing. From these numerical experiments, we find that both a Maxwell and Kelvin-Voigt model for ice reduce the rate of crevasse propagation as compared to a linearly elastic model. This implies that crystal plastic processes relax stress around crevasses and therefore controls the rate of crack growth in ice-shelves. The results of crevasse evolution, as governed by elastic and viscoelastic end-member cases, indicate that the viscous response of ice plays a significant role in crack propagation—highlighting the importance of incorporating descriptions of crystal plasticity in predictions of crevasse development.