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We consider a theory for shallow ice shelves that includes an isotropic damage variable. A zeroth-order shallow-shelf approximation allows a simple yet consistent treatment of both ice dynamics and damage evolution. We find that the damage variable (like temperature) has, in general, to vary with depth; a purely two-dimensional membrane theory can only be considered a rough approximation for isothermal ice shelves.
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Keller et al. (2014) studied this question.
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