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From work by JONGMIN SHIM, KATIA BERTOLDI AND PEDRO REIS
News feature article in Nature, August 8, 2012, by Kim Krieger, Nature, Vol 488, pp. 146-147, DOI: 10.1038/488146a
"Katia Bertoldi is talking fast. She has only 12 minutes to present her work in the burgeoning field of 'extreme mechanics'. But first, the Harvard University engineer smiles at the physicists gathered in Boston at the March 2012 meeting of the American Physical Society. She has to show them what she found in a toy shop.
Projected onto the screen, the Hoberman Twist-O looks like a hollow football made of garishly coloured plastic links. Twist it just so, however, and hinges between the links allow it to collapse into a ball a fraction of its original size. Twist it the other way, and it springs back open. Bertoldi explains that the Twist-O inspired her group to create a spherical device that collapses and re-expands, not with hinges but through mechanical instabilities: carefully designed weak spots that behave in a predictable way. Applications might include lightweight, self-assembling portable shelters or nanometre-scale drug-delivery capsules that would expand and release their cargo only after they had passed through the bloodstream and reached their target.
The challenge, Bertoldi says, is to figure out the exact instabilities a structure needs to achieve its desired behaviour. She quickly describes the necessary geometry and runs down a list of constraints. There are just 25 shapes that satisfy all the requirements, she explains, glossing over the months of computation it took to solve the problem. Then she starts a video to show the assembled throng the design that her team has come up with.
An image of a rubbery chartreuse ball with 24 carefully spaced round dimples (pictured) materializes on the screen. The test begins and the ball slowly collapses, each dimple squeezing shut as the structure twists into a smaller version of itself. There is a moment of silence, then everyone in the room begins to clap.
Student engineers have always been taught that mechanical instabilities are a problem to avoid. Such instabilities can quickly lead to structural failures — the collapse of a weight-bearing pillar, the crumpling of a flat steel plate or the buckling of a metal shell. From failures come disasters, such as the Second World War Liberty Ships that broke up while at sea. And the devilishly complex mathematical analysis of buckling structures ground to a halt in the late nineteenth century, because it was unworkable with the methods then available.
During the past half-decade or so, however, a new generation of physicists and engineers has begun to embrace instability. These researchers have been inspired, in part, by advances in geometry and nonlinear mathematics that have allowed them to progress where their forebears could not. They have already, for example, devised a theory for why cabbage leaves and torn plastic rubbish bags ripple; calculated the patterns of wrinkles in fabric and crumples in paper; and accounted for the way coils and loops develop in the guts of vertebrate embryos.
More on the website:
http://www.nature.com/news/extreme-mechanics-buckling-down-1.11127
See the journal article:
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.
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.
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