Stress Condensation in Crushed Elastic Manifolds

We discuss an M-dimensional phantom elastic manifold of linear size L crushed into a small sphere of radius R in N-dimensional space. We investigate the low elastic energy states of 2-sheets (M0ex{0ex}=0ex{0ex}2) and 3-sheets (M0ex{0ex}=0ex{0ex}3) using analytic methods and lattice simulations. When N2M the curvature energy is uniformly distributed in the sheet and the strain energy is negligible. But when N0ex{0ex}=0ex{0ex}M+1 and M>1, both energies appear to be condensed into a network of narrow M-1 dimensional ridges. The ridges appear straight over distances comparable to the confining radius R.