Buckling induced by dilative strain in two- and three-dimensional layered materials

Buckling of stripes in two dimensions, or layers in three dimensions, induced by dilative strain, is observed in thin films, in liquid crystals, and at interfaces. Equations for the buckling pattern are analyzed and solved in this work. We have previously predicted buckling patterns in two-dimensional systems, which were subsequently successfully compared with experiment. Here we make predicted buckling profiles for three-dimensional layered materials available for comparison with experiment. We also analyze dilative strain-induced buckling on a qualitative level, in terms of mechanical analogy, and compare the modulation pattern with that which arises in other contexts.