Curvature-driven morphing of non-Euclidean shells. (31st May 2017)

• Record Type: Journal Article
• Authors: Pezzulla, Matteo; Stoop, Norbert; Jiang, Xin; Holmes, D. P.
• Is Part Of: Proceedings. Volume 473:Number 2201(2017)
• Publication Date: 2017-05-31
• Subjects: swelling -- curvature -- shells -- geometry -- morphing; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2017.0087
• Languages: English
• ISSNs: 1364-5021

Abstract

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.