Ice shelf fracture is responsible for roughly half of Antarctic ice mass loss in the form of calving and can weaken buttressing of upstream ice flow. Large uncertainties associated with the ice sheet response to climate variations are due to a poor understanding of these fracture processes and how to model them. Here, we address these problems by developing an anisotropic, nonlocal, creep damage model for large-scale shallow-shelf ice flow. This model can be used to study the full evolution of fracture from initiation of crevassing to rifting that eventually causes tabular calving. While previous ice shelf fracture models have largely relied on simple expressions to estimate crevasse depths, our model parameterizes fracture directly in 3-D. We also develop an efficient supporting numerical framework based on the material point method, which avoids advection errors. Using an idealized marine ice sheet, we test our methods in comparison to a damage model that parameterizes crevasse depths, as well as a modified version of the latter model that accounts for how necking and mass balance affect damage. We demonstrate that the creep damage model is best suited for capturing weakening and rifting, and that anisotropic damage reproduces typically observed fracture patterns better than isotropic damage. However, we also show how necking and mass balance can significantly influence damage on decadal timescales. Because these processes are currently absent from the creep damage parameterization, we discuss the possibility for a combined approach between models to best represent mechanical weakening and tabular calving within long-term simulations.

We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and ice thickness evolution equations. We introduce novel numerical schemes for particle splitting and integration at domain boundaries to accurately simulate the spreading of an ice shelf. The advantages of the proposed GIMPM-SSA framework include efficient advection of history or internal state variables without diffusion errors, automated tracking of the ice front and grounding line at sub-element scales, and a weak formulation based on well-established conventions of the finite element method with minimal additional computational cost. We demonstrate the numerical accuracy and stability of the GIMPM using 1-D and 2-D benchmark examples. We also compare the accuracy of the GIMPM with the standard material point method (sMPM) and a reweighted form of the sMPM. We find that the grid-crossing error is very severe for SSA simulations with the sMPM, whereas the GIMPM successfully mitigates this error. While the grid-crossing error can be reasonably reduced in the sMPM by implementing a simple material point reweighting scheme, this approach it not as accurate as the GIMPM. Thus, we illustrate that the GIMPM-SSA model is viable for the simulation of ice sheet-shelf evolution and enables boundary tracking and error-free advection of history or state variables, such as ice thickness or damage.