A numerical technique called the material-point method (MPM) shows promise for treating problems of ice dynamics. MPM is based on particle-in-cell technology and thus uses 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. Example calculations are performed for a rectangular region of Arctic ice using a newly-developed elastic-decohesive constitutive model. In the simulations, the ice motion is wind-driven and resisted by ocean drag. Two adjacent sides of the rectangle are rigid shorelines and the other two edges are free surfaces that can deform freely. These MPM calculations are compared with published finite element simulations using a viscous-plastic rheology.
The pack ice is effected by both thermodynamic and mechanical processes. Thermodynamic processes result in mass changes at the atmosphere and ocean boundaries. Mechanical processes can result in the formation of leads and pressure ridges, for example. Motion of the ice pack is driven by the atmosphere and ocean. The ice pack is able to move and deform because of concentrated deformations at leads. Leads form and new areas of open water are exposed. When the driving forces cause the ice to converge, convergence is accommodated by closing open water, and, if necessary, rearranging thin ice by rafting or ridging. An elastic-decohesive constitutive-model for pack ice has been developed that explictly accounts for leads (Schreyer et al., 2006). The constitutive-model 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. Several features were designed into the model.
