## 1 Introduction

[2] Calving is an important process in marine-terminating glaciers, including Antarctic ice shelves and Greenland outlet glaciers, accounting for as much as half of the mass lost from the Antarctic and Greenland ice sheets [e.g., *Jacobs et al.*, 1992; *Biggs*, 1999; *Rignot et al.*, 2008]. The processes that cause iceberg detachment, however, are complex, involving the initiation and propagation of fractures over spatial scales ranging from crystal-sized defects to rifts systems in ice shelves that span hundreds of kilometers. Although the initiation and propagation of crevasses and rifts within glaciers and ice shelves are clearly linked to flow dynamics over a wide range of environmental conditions and flow regimes, we do not yet have a well-formulated mathematical model of iceberg calving [*Van der Veen*, 2002; *Bassis et al.*, 2005; *Benn et al.*, 2007; *Bassis*, 2011; *Bassis and Walker*, 2012]. This suggests that success in incorporating iceberg calving into the next-generation ice sheet models hinges on formulating (and testing) a physical model of the fracture process that enables us to simulate crevasse propagation.

[3] The depth to which surface crevasses penetrate was first estimated using the Nye zero-stress model in which surface and bottom crevasses penetrate to the depth where the net horizontal stress vanishes [*Nye*, 1957; *Jezek*, 1984; *Nick et al.*, 2010]. The Nye zero-stress model typically assumes that glacier ice has no tensile strength, a hypothesis at odds with both field- and laboratory-derived studies of the strength of ice [*Schulson and Duval*, 2009]. An alternative approach uses linear elastic fracture mechanics (LEFM) which assumes that ice behaves like a brittle elastic solid and fractures initiate from small, sharp “starter cracks” assumed to be always present within the ice [*Lawn*, 1993]. However, LEFM is only appropriate for modeling instantaneous crevasse propagation over a shorter time scale associated with brittle elastic behavior but not for modeling creep-induced crevasse propagation over a longer time scale associated with significant viscous deformation. Moreover, the discontinuous nature of (linear elastic) fracture makes it difficult to self-consistently integrate crevasse initiation and propagation into viscous ice dynamics models.

[4] An alternative approach involves the use of continuum damage mechanics. Unlike other methods that focus on initiation and propagation of individual fractures in ice, this technique models the evolution of many distributed “flaws” within the ice and their effect on its bulk rheology. Previously, *Pralong et al.*[2003, 2005] employed the notion of continuum damage and assumed that ice behaves as an incompressible viscous fluid to study crevasse propagation. However, this approach neglects the elastic stress effects and uses a local creep damage formulation that yields mesh-dependent and inconsistent results [*Murakami and Liu*, 1995]. A nonlocal damage formulation eliminates the unrealistic singular localization of damage and alleviates the pathological mesh dependence of finite element calculations by introducing a length scale for damage [*Bazant and Pijaudier-Cabot*, 1988].

[5] In this paper, our aim is to investigate the conditions that enable surface crevasse propagation using a nonlocal viscoelastic damage model. We consider the nonlinear viscoelastic material behavior of ice [*Glen*, 1955] and creep damage evolution due to the progressive accumulation of microcracks in tension [*Murakami*, 1983], under sustained gravity loading. Eventually, the microcracks coalesce to form one macrocrack, leading to tensile creep fracture. The main advantage of this computational model is that it is only necessary to specify glacier geometry and boundary conditions (at the glacier base and on the ice-ocean boundary); the stress field in the glacier and its damage state, due to gravity and hydrostatic seawater pressure, are computed using the finite element method. Additionally, using the displacement field results from the simulations, we can estimate the strain rate and flow velocity of ice.