A thermodynamic formulation for pack ice is presented that includes a means of relating stresses in floes to thermally-induced strain rates. The formulation combines some basic thermodynamics as well as a mechanics component which includes viscous creep and mechanically induced strain rates due to typical floes being too large to bend or twist in response to spatially varying strain rates. Moreover, the rheology quantifies the impact of existing cracks in the floe on the overall strain rate in the floe and the resulting stress state. A paradigm is put forward which specifies tensile fracturing and the resulting stress relief as being proportional to the amount of existing cracks and some measure of the tensile strength of the ice in the floe. This allows the thermomechanical equations to be used for both first-year and multi-year floes by differentiating the two by the extent of existing cracks.
In addition to the body of work on the thermodynamics of sea ice, a great deal of work has been performed dealing with the mechanics of pack ice. The two topics are closely related in that thermal forcing can cause significant stresses and fracturing in pack ice. In this work, an attempt is made to provide a thermo-mechanical formulation that combines the more basic thermodynamic processes in a floe with a rheology relating thermally-induced strain rates to the stress state within the floe. Crossing over from pure thermodynamics to thermomechanics is complicated by the fact that we do not have a definitive relationship between the stressing and fracturing of pack ice. In addition, observations of thermo-mechanical processes in first-year and multi-year floes are quite different even for identical thermal forcing. Here we will provide the basic formulation for the thermodynamics and then concentrate on the details of the mechanics.
