## Geometrically incompatible confinement and elastocapillary phenomena

Confining thin objects, such as rods, sheets and shells, into a volume smaller than their lateral size typically generates in them stress. Relaxation of this stress often gives rise to the complex deformations –wrinkles, crumples, and folds– which are characterized by a multitude of spatial scale, indicating on a hierarchical structure of elastic energy.

In this talk I will present examples of “geometrically incompatible” confinement of solid sheets –the wrapping of a rigid ball, and the contact of liquid volume with a stretched plate– whereby some level of strain is unavoidable. These examples demonstrate the nontrivial nature of the energetic hierarchy that underlies shape deformation and the distribution of stress in such problems. In particular, I will present a novel variational principle, the “Gauss-Euler elastica”, which generalizes the classical Euler elastica to a class of geometrically-incompatible confinement problems.