Deborah Sulsky
Department of Mathematics and Statistics
Department of Mechanical Engineering
University of New Mexico
A new model for the Arctic pack ice will be presented in which the deformation of ice is based mainly on motion due to formation of leads. That is, pack ice is assumed to be fairly rigid and brittle; it responds to forcing by breaking apart, moving and refreezing. The constitutive model for pack ice is based on elasticity combined with a cohesive crack law that predicts the initiation, orientation and opening of leads, and also has a simple closing model. The model is constructed to transition from observed brittle failure under tension, to compressive brittle failure under moderate compression, and to a plastic-like faulting under large confinement [1]. The various modes of failure occur in the model, depending on the stress state in the ice. Where the transitions occur in stress space depends on the material parameters and can be adjusted based on empirical data.
Example calculations using the elastic-decohesive constitutive model will be shown for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic. Numerical solutions of mechanics problems where cracks are explicitly included are notoriously difficult to obtain robustly. A numerical technique called the material-point method (MPM) shows promise for treating this class of problems. MPM is based on a Lagrangian set of material points with associated mass, position, velocity, stress, and other material parameters, and a background mesh where the momentum equation is solved. This method avoids the convection errors associated with fully Eulerian methods as well as the mesh entanglement that can occur with fully Lagrangian methods under large deformations.
[1] E. M. Schulson. Compressive shear faults within Arctic sea ice: Fracture on scales large and small. Journal of Geophysical Research-Oceans, 109(C7):C07016, JUL 2004.