Colloquium: Tuesday June 10, 2025. Speaker: Raz Kupferman (HUJI). Title: “Non-Euclidean elasticity: Review and current challenges”.
The most rudimentary description of an elastic body is as a Riemannian manifold (with boundary) constrained to “live” in an ambient Euclidean space of same dimension. To each configuration (i.e., to each embedding of the body in space) is assigned an energy, measuring a geometric discrepancy between the body and its image. Equilibrium configurations are postulated to be minimizers of that energy, thus posing a problem within the realm of the calculus of variations. Classical elasticity has been concerned with elastic bodies that are Euclidean, in which case the variational problem is non-trivial only when supplemented with extra forces, or boundary constraints. Recent years have seen much interest in elastic bodies assuming non-trivial geometries and topologies, motivated by experiments and even industrial applications. In this lecture I will review some more and less recent advances in the field of so-called non-Euclidean elasticity, as well as some remaining challenges. No prior knowledge in physics or material science is assumed.
