Ginzburg-Landau theory may be thought of as the relaxation of the Dirichlet energy for maps into the circle. Sticking to this interpretation, what I will present in this talk are some results on the relaxation of the Dirichlet energy of O(2,3)-valued maps with a gradient constraint, and variants of this functional. Here O(2,3) denotes the set of linear isometries from two- to three-dimensional Euclidean space. These variational functionals can be interpreted as models for thin elastic sheets, and in particular crumpled structures.