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Creep and recrystallization of large polycrystalline masses Part III: Continuum theory of ice sheets
Sérgio H. Faria
This work presents the first thermodynamically consistent constitutive theory for ice sheets undergoing strain-induced anisotropy, polygonization and recrystallization e ects. It is based on the formalism of mixtures with continuous diversity, by picturing the ice sheet as a huge mixture of crystallographic orientations . The fabric (or texture) is described by an orientation-dependent field of mass density which is sensitive not only to the lattice spin, but also to changes in the shape of the grain size distribution. No constraint at all is imposed on the stress or the strain of single crystallites, except that basal slip is considered the dominant deformation mechanism and grain boundary sliding is negligible. Curiously, despite the fact that individual ice crystallites are regarded as micropolar media, it is inferred that couples on distinct grains counteract each other, so that polycrystalline ice sheet particles behave as ordinary (non-polar) continua. Several concepts from materials science are derived within the framework of the continuum theory, e.g. the lattice distortion energy, the grain boundary mobility and the Schmid tensor, as well as some fabric (texture) parameters like the degree of orientation of the fabric and its 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 di erences in the dislocation potentials (viz. the Gibbs free energies due to dislocations) of crystallites with distinct c-axis orientations. Finally, a generalization of Glen s flow law is derived and compared with former generalizations found in the literature, like the Svendsen G¨odert Hutter stress law and the Azuma Goto-Azuma flow law.