Phase field approach to model fracture propagation in sea ice
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The thin layer of ice that covers the polar oceans is a complex geomaterial that is perpetually stressed and fractured by winds and ocean currents. To represent this brittle behavior, current sea-ice models rely on a progressive damage approach, in which fracture density evolves as a function of the local state of stress. While computationally efficient, this approach does not explicitly capture single crack nucleation, propagation, nor evolving crack geometry. With the aim of providing a more physically accurate description of the transition from the intact to the fragmented state and, thereby, an improved representation of the evolving mechanical properties of sea ice through this transition, we develop a simple phase-field framework to resolve crack initiation, interaction and the resulting granularization of the material under compressive shear, the most common mode of loading within sea ice. The model employs a double-well energy formulation following Karma et al. (2001), coupled with an overdamped displacement field for the elastic response. The governing equations are solved using a spectral method in Fourier space. We successfully test this framework against a benchmark mode I fracture experiments: the opening of an inclusion in an elastic matrix under tensile forcing following the Griffith’s criteria of fracture propagation. Additional configurations are investigated to study fracture nucleation and propagation under a shear body force, including an inclusion solicited under simple plane shear and a cylindrical Couette experiment for which the analytical solution of the displacement field is well-known. We present these results along with an investigation of the impact of energy decomposition on the crack geometry under shear loading.
