Confined curved shells and their elaborate conformations

Curved shells, when confined, can deform to a broad assortment of large scale shapes and smaller scale wrinkling and folding patterns quite unlike those produced by their flat counterparts. The intrinsic, natural curvature of an elastic shell is the central element that allows for this rich and very interesting morphological landscape. It is also the source of the geometric nonlinearities that render a direct analytic treatment of non-Euclidean shells difficult, even under small forces or applied loads. In this talk we examine some snapshots of this morphological landscape. Inspired by the natural folding and unfolding of pollen grains, we use theory, simulations and experiments to explore the large scale deformation of a confined thin spherical shell with an opening. We then proceed to investigate the surface topography of shallow doubly curved shells resting on a fluid substrate. The frustration due to the competing flat geometry of the substrate and the curved one of the shell produces a wealth of highly reproducible and ordered wrinkling patterns, in conjunction with other random and disordered patterns as well. These examples illustrate that Gaussian curvature can be a powerful tool for the creation of complex patterns