A theoretical framework is developed, which relates small-scale pack ice energy transformations dominated by ridging and sliding processes to large-scale dynamics described by internal ice stress and strain rate. The framework consists of an energy equation, a kinematic model, and the minimization of maximum shear stress. From the kinematic model and energy equation we derive an expression for the maximum shear stress and compressive stress in terms of a deformational pattern and geometry of cracks. For each choice of a kinematic model the minimization principle applied to this expression gives an explicit constitutive relationship as follows: a yield curve, a flow rule, and the directional relationship between stress and strain rate. The theory provides an energetic explanation for different yield curves and flow rules. The cavitating fluid is realized with the absence of energetic transformations on shear and divergent motions. Hibler's (1979) constitutive relationship corresponds to the energetic function whose form depends on the strain rate magnitude, reflecting the viscous-plastic coupling.

It is found that for a class of energy functions associated with smooth and strictly convex yield curves the flow rule is normal. The Mohr-Coulomb yield criterion is identified as a special case of the normal flow rule. Preferred orientation of cracks is also explained by the same minimization of the maximum shear stress. The theory predicts that the preferred orientation depends on ice geometry, as well as the energetic contribution from sliding relative to ridging. For uniform square- and diamond-shaped floes the maximum shear stress associated with ridging obtains its minimum value when the axes of symmetry of the floes coincide with the principal axes of the strain rate. A field of isotropically oriented square-shaped floes is simulated, resulting in a sine lens-shaped yield curve. ¿ American Geophysical Union 1994