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From:
http://www.pnas.org/content/109/16/5978/F1.expansion.html
From work by JONGMIN SHIM, KATIA BERTOLDI AND PEDRO REIS
Proceedings of the National Academy of Science (PNAS), Vol. 109, No. 16, pp. 5976-5983
Full caption of the image:
Fig. 1. Sequence of progressively deformed shapes. (A) Hoberman’s Twist-o, a commercial toy, compressed by hand. (B) Buckliball, made of silicone-based rubber, pressurized by a motorized syringe pump. (C) Finite element simulations for the Buckliball. (Scale bars: 3 cm.)
The paper:
Jongmin Shim (1), Claude Perdigou (2), Elizabeth R. Chen (3), Katia Bertoldi (1), and Pedro M. Reis (2)
(1) School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 021383;
(2) Departments of Mechanical Engineering and Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; and
(3) Department of Mathematics, University of Michigan, Ann Arbor, MI 48109
“Buckling-induced encapsulation of structured elastic shells under pressure”, Proceedings of the National Academy of Sciences of the United States of America (PNAS), Vol. 109, No. 16, pp. 5978 – 5983, 2012.
ABSTRACT: We introduce a class of continuum shell structures, the Buckliball, which undergoes a structural transformation induced by buckling under pressure loading. The geometry of the Buckliball comprises a spherical shell patterned with a regular array of circular voids. In order for the pattern transformation to be induced by buckling, the possible number and arrangement of these voids are found to be restricted to five specific configurations. Below a critical internal pressure, the narrow ligaments between the voids buckle, leading to a cooperative buckling cascade of the skeleton of the ball. This ligament buckling leads to closure of the voids and a reduction of the total volume of the shell by up to 54%, while remaining spherical, thereby opening the possibility of encapsulation. We use a combination of precision desktop-scale experiments, finite element simulations, and scaling analyses to explore the underlying mechanics of these foldable structures, finding excellent qualitative and quantitative agreement. Given that this folding mechanism is induced by a mechanical instability, our Buckliball opens the possibility for reversible encapsulation, over a wide range of length scales.
Comment by D. Bushnell:
The main component of deformation in the top row appears to be in-plane rotation of each of the little cruciform elements of which the spherical toy is constructed.
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