Multistable Slit Caps

Abstract

Multistable shells are structures that have more than one stable state of self-stress. We demonstrate for the first time that an initially stress-free, hemispherical cap with isotropic behaviour can gain at least three additional stable shapes and, hence, states of self-stress, if it is sliced partially along a given axi-symmetrical meridian. The usual initial and inverted configurations are only slightly affected by slicing. The other configurations are elicited by extra deformations about the inverted shape, which now performs a pre-stressing role. The experimental results are confirmed by finite-element simulations, and it is shown that initially rotationally symmetric structures can gain three stable configurations. Motivated by this, a simplified analytical approach using Foppl-von Karman plate theory is undertaken to analyse the bistable properties of shallow spherical segments. It is shown that the boundary conditions have a dominating influence on the occurrence of multistability.