Elastic platonic shells
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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