title: Elastic platonic shells.
abstract: On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Ee Hou
authors.initials: EH
authors.lastname: Yong
authors.forename: David R
authors.initials: DR
authors.lastname: Nelson
authors.forename: L
authors.initials: L
authors.lastname: Mahadevan
mesh_terms: D003460:Crystallization; D004548:Elasticity; D008956:Models, Chemical