Multistable corrugated shells

Abstract

We have been constructing and investigating multistable corrugated shell structures. The multistability arises from the interaction between internal prestresses created during forming and nonlinear geometrical changes during deformation. Using a simplified analytical elastic model, we homogenize the properties of the shells through simultaneously considering the material on two scales: the ‘local’ scale of the isotropic material; and the ‘global’ scale of the corrugated sheet, which is then modelled as an equivalent flat sheet with anisotropic properties. This model is applied to simulate two modes of bistability observed in prototypes: first, prestressed corrugated shells that, when buckled, can coil up into a tube repeatably and reversibly; and second, corrugated sheets with a symmetry-breaking ‘twisting’ curvature. The model gives an intuitive understanding of the behaviour, and has enabled us to understand forming processes that give the behaviour we wish, including tristable shells that combine both bistable modes.