Curvature-Driven Morphing of Non-Euclidean Shells

TL;DR

This paper develops a geometrical model to understand how non-mechanical stimuli induce shape changes in non-Euclidean shells, with applications to various structures like plates, shells, cylinders, and cones, showing excellent agreement with numerical simulations.

Contribution

The paper derives a scalable, purely geometrical model linking stimuli to shape changes in non-Euclidean shells, extending the theory of non-Euclidean plates and shells.

Findings

Cylinders and cones can bend, unroll, snap, and rotate under stimuli.

The model accurately predicts shape changes in spherical shells and other structures.

Shape transformations are governed by the geometry of the structure, not material specifics.

Abstract

We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly-isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.