Orientational order in buckling elastic membranes

We study pattern formation in buckling membranes under lateral compression, using the Föppl–von Kármán (FvK) approximation for nonlinear elasticity. To identify the role of shear strain, we numerically compare the patterns on elastic and fluid membranes as well as their coarsening dynamics. By mapping the FvK equations onto a vector spin model with nonlocal interactions, we find anisotropic correlation of ridges that characterizes the topography of crumpled elastic membranes.