Folding energetics in thin-film diaphragms

We perform experiments to elucidate how the folding patterns of thin-film diaphragms subject to in-plane isotropic and anisotropic compressive strains depend on the shape, thickness and size of the diaphragms. We then use a constrained von Kaármaán model to relate the experimental results to the energetics of folding. We show that the differences between the isotropic and the anisotropic cases can be traced back to the structure of the membraneous energy density function. In the isotropic case, we find foldings which satisfy the boundary conditions and minimize the membraneous energy. In the anisotropic case, no such foldings exist, but we are able to construct sequences of increasingly fine foldings which satisfy the boundary conditions and whose membraneous energies converge to the infimum. In both cases, we obtain solutions by allowing bending to select a preferred folding. The solutions compare well with the experimental observations.