Wrinkling formation is a central topic in morphogenesis and material science. The exchange of energy from stretching to bending acts as a paradigm for a wide range of elastic instabilities, including the wrinkling of the gut, and the crinkling of leaves. It has been extensively studied under the assumption that the change of the metric is negligibly small (or irrelevant). We are developing a combination of experiments, numerical methods, and analytical results that indicate that this paradigm is not general.
In two dimensions this type of problem is typically considered by the model of an elastica in compressive confinement. We show that, even without any external forces, an elastic surface supported by a fluid can bend and wrinkle when it acquires a non-zero natural curvature. Locally, we can demonstrate how a preferential curvature can be related to an effective compression, and hence a confining force that can vary spatially. This suggests a simple experimental setup, where we have characterized a variety of wrinkle patterns that can be generated for different mechanical properties and natural curvatures.
When a soft naturally curved film is placed on a liquid interface it deforms dramatically. The resultant configurations have strong connections with a large variety of elastic instabilities. For instance, sharp structures in the patterns are related to topological frustrations typically seen in crumpled papers. To avoid stretching, solid surfaces preserve their metric, leading to the concentration of the energy in strongly bent regions (vertices). However, depending on the stiffness, the metric of the film may eventually change. Then, a peculiar phenomenon takes place: sharp structures disappear and a smooth wrinkling pattern emerges. By making transparent the films and using Schlieren photography, we want to perform direct measurements of the curvature fields and establish the local states of the metric. In addition, we want to recognize proper order parameters and construct phase diagrams of the resulting patterns.