Shape formation via elastic instabilities

When a solid object is placed under a load, it will deform to a new shape. Typically, these shape changes are modest and predictable, but sometimes, when a critical load is reached, the object will undergo an elastic instability and adopt a dramatically different and more complicated shape. Traditionally, elastic instabilities, such as buckling and wrinkling, have been studied as failure modes in stiff material systems. However, soft highly deformable solids, such as rubbers and biological tissues, can undergo instabilities without failure, offering the opportunity to utilize instabilities to change their shape. Furthermore, the largestrain mechanics of soft solids introduces many new instabilities not seen in traditional materials. Evolution is known to exploit soft elastic instabilities to sculpt brains, guts and other developing organs, and human engineers are interested in using them to create shape switching devices. There is a pressing need to understand what types of elastic instability exist, what shapes they form, and how these shapes can be controlled. In this thesis, I address each of these challenges. I first present a new elastic instability, in which a cylindrical channel through a soft solid adopts a peristaltic shape upon loading with sufficient internal pressure. I then present a theory of pattern selection in surface elastic instabilities, including the compressive wrinkling of a stiff sheet on a soft substrate, and the gravitational fingering of a soft gel layer. Using higher order perturbation theory, I find, in both cases, that patterns of hexagonal dents are favoured, and I present a symmetry argument that hexagonal patterns are generic. Finally, I present a technique to manipulate the patterns formed in layer/substrate buckling by patterning the system with holes. This simple technique shows that instability patterns can be designed, opening new engineering opportunities