In this chapter we have studied four classical problems in glacier mechanics: closure of cylindrical holes, calculation of force balances, creep of ice shelves, and deformation of boreholes. As examples of applications of the theory presented, we discussed problems such as the flow of water to, from, and in subglacial conduits, the mechanics of glacier accelerations, the stability of ice shelves, and the extraction of flow-law parameters from borehole deformation data. From these examples, we gained insights into the dynamic and kinematic behavior of glaciers. These, however, were secondary objectives.

The primary objective of the chapter was to help students develop facility with the mathematics of stress and deformation as applied to problems in glacier mechanics. Such analyses are complicated because multiple stresses, strains, and strain rates are involved, and even more so because the strains in which we are interested are a consequence of deviatoric, not total stresses. In many cases, once the physics of a problem have been formulated, prescribed mathematical procedures must be followed before a result with clear physical significance reappears. Students who have mastered the material in this chapter will be able to understand many papers in the glaciological literature that would otherwise be impenetrable.

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