This chapter presents a brief treatment of problems defined on thin structures. A scaling argument allows the expression of the problem as an asymptotic study of degenerate energies on a single set. It is shown that the limit energy is independent on the ‘thin dimension’, and thus it is a dimensionally-reduced energy. In the convex case, the limit energy density is obtained by an optimization of a problem involving the original energy. An example shows that the same formula does not hold if the energies are polyconvex, and an additional quasiconvexification process is needed as in the theory of LeDret and Raoult.
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