Creep and recrystallization of large polycrystalline masses. III. Continuum theory of ice sheets

This work sets forth the first thermodynamically consistent constitutive theory for ice sheets undergoing strain-induced anisotropy, polygonization and recrystallization effects. It is based on the notion of a mixture with continuous diversity, by picturing the ice sheet as a ‘mixture of lattice orientations’. The fabric (texture) is described by an orientation-dependent field of mass density which is sensitive not only to lattice spin, but also to grain boundary migration. No constraint is imposed on stress or strain of individual crystallites, aside from the assumption that basal slip is the dominant deformation mechanism on the grain scale. In spite of the fact that individual ice crystallites are regarded as micropolar media, it is inferred that couples on distinct grains counteract each other, so that the ice sheet behaves on a large scale as an ordinary (non-polar) continuum. Several concepts from materials science are translated to the language of continuum theory, like, for example, lattice distortion energy , grain boundary mobility and Schmid tensor , as well as some fabric (texture) parameters like the so-called degree of orientation and spherical aperture. After choosing suitable expressions for the stored energy and entropy of dislocations, it is shown that the driving pressure for grain boundary migration can be associated to differences in the dislocation potentials ( viz . the Gibbs free energies due to dislocations) of crystallites with distinct c -axis orientations. Finally, the generic representation derived for the Cauchy stress is compared with former generalizations of Glen's flow law, namely the Svendsen–Gödert–Hutter stress law and the Azuma–Goto–Azuma flow law.