10.1098/rspa.2001.0921 Folding energetics in thin-¯lm diaphragms

We perform experiments to elucidate how the folding patterns of thin- lm dia-phragms 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 K´arm´an model to relate the experimental results to the energetics of folding. We show that the di¬erences 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 nd 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 ne foldings which satisfy the boundary conditions and whose membraneous energies converge to the in mum. In both cases, we obtain solutions by allowing bending to select a preferred folding. The solutions compare well with the experimental observations