Compliant shell mechanisms and the geometry of isometric deformations

Abstract: Maxwell, later improved on by Calladine, famously counted the ways in which a truss can deform without stretching its members. Here, we want to do something similar but for (1) shells, (2) that are roughly flat such as wrinkled membranes, corrugated plates, and origami tessellations, (3) assuming they have no holes or handles. Stretch-free, we say isometric, deformations are important because they cost very little energy: we desire them when we want the shell to change shape easily, and we fear them when we want the shell to be structurally stable. We will report on recent results on the geometry of isometric deformations: not so much what they look like for specific shells, but rather how they fit together in one abstract space. For instance, we show that if the shell is soft in shearing, then it is stiff in twisting; if it is soft in bi-axial compression in the plane then it is stiff in synclastic bending out of plane; and so on. These properties are formalized thanks to a symplectic form and to a bunch of universal algebraic identities that make appear the shell’s elasticity moduli. Proofs will take us on a journey from graphical statics to the theory of composites and rely on ideas introduced by prominent figures of solid and structural mechanics such as, well Maxwell of course, but also Airy, Pucher (or Laplace, we can choose), Hill and Mandel.

Le mercredi 27 mai 2026 à 11h00 / Amphithéâtre François Canac, LMA

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