On shape and elasticity: bio-sheets, curved crystals, and odd droplets

Because thin systems can deform along the thickness with relative ease, the interplay between surface mechanics and geometry plays a fundamental role in sculpting their three-dimensional shape. Often, deformations arise as a consequence of elastic pre-stress in the material, for example because of the small-scale geometry of the constituents or their local arrangement. In this thesis, we look at the connection between geometry, local and global, and mechanics in thin closed shells and open sheets which we consider as two-dimensional solids that we study using linear elasticity theory. In particular, we investigate the elasticity-driven shape deformations in the context of three soft matter systems: dense single-layered crystals, oil-in-water emulsions, and biological thin assemblies of tubulin. Theoretical Physic