Fracture propagation in glaciers using discontinuous Galerkin finite element methods

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Iceberg calving is a complex, yet natural fracture process and is responsible for half of the mass lost from thefloating ice shelves and marine-terminating glaciers (i.e., marginal ice zones) in Greenland and Antarctica. There ismajor concern that rapid changes in the marginal ice zones due to calving linked to climate dynamics can destabilizethe Antarctic and Greenland ice sheets. It has been hypothesized that hydrofracturing of ice shelves followedby ice cliff failure in Antarctica could contribute to rapid sea level rise over the coming centuries. Therefore, itis essential that we improve our understanding of the fracture mechanics of iceberg calving and its representationin large-scale numerical models, in order to better predict the evolution of Greenland and Antarctica ice sheets.Linear elastic fracture mechanics (LEFM) based iceberg calving representations have been deployed within ice sheetmodels. However, simulating fracture propagation using LEFM with standard finite elements can be computa-tionally inefficient. Recent advances in Phase Field (PF) damage models have shown great promise for simulatingfracture propagation. PF models represent fractures through a damage-like scalar variable which is modelled asa separate spatially varying field. The PF varies smoothly between 0 for intact (undamaged) material to 1 for fullycracked parts of the domain and the value of this field is coupled to the stiffness of the parent material. However,these models are at a preliminary stage of development for simulating mixed-mode fracture propagation, especiallyunder multiaxial stress states. Several advancements are needed to establish the viability of the PF model for captur-ing the complexity of iceberg calving process from glaciers. On the damage modelling front, new crack driving forceformulations are needed to accurately describe hydromechanical fracture under multiaxial compressive stress states.On the numerical method front, new techniques/algorithms are needed to efficiently simulate 3D crack propagation.The goal of this project is to develop a new computational approach for the accurate and efficient simulation ofmixed-mode fracture propagation in glacier ice using a PF model implemented with a mesh-adaptive discontinousGalerkin finite element method (DG-FEM). The Durham supervision team, Prof. Coombs and Dr Giani, areexperts in developing and testing novel numerical methods, including the DG-FEM . The main advantageof the DG-FEM is that it can efficiently simulate the evolution of the PF (and the stress field), via hp adaptivemesh refinement. The project will also be supported by Prof. Ravindra Duddu (Vanderbilt University, USA) whois an expert in computational fracture, including the PF damage models, and ice sheet modelling .This PhD project will develop a numerical framework for large-scale analysis ice fracture via DG-FEM techniquesin 3D. One of the current limitations of existing PF models is their computational cost, driven by the need forsufficient elements in the damaged region. As the length scale controlling the width of the damage zones is reduced,which provides a more accurate fracture representation, the element size must be reduced in the same proportionAs the fracture network is unknown a priori, many researchers resort to using a fine computational meshthroughout the analysis - this is excessively wasteful. This project follow a different approach via error-estimatedriven mesh adaptivity, allowing for highly accurate fracture predictions whilst remaining computationally tractable.