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Puppeteering is the art of pulling and pushing strings and rods to cause a puppet to move in a coordinated fashion. The puppeteer\u2019s job is not very different from that of a physicist, engineer, or materials scientist, who commonly seek to convert input forces into resulting motions. When making puppets dance, puppeteers have an advantage over physicists, however: they make use of learned intuition and expertise \u2013 rather than mathematics \u2013 to coordinate their pushes and pulls in real time.<\/p>\n\n\n\n
For the physicist, predicting the pronounced (or in more technical terms: nonlinear<\/em>) deformations of elastic objects is a difficult game, where progress is slow. Precise recipes to choose input pushes and pulls to produce the desired deformation \u2013 the dance of the puppet \u2013 are quite rare. This is what makes the \u201cpuppetry\u201d achieved in the paper \u201cConformal Elasticity of Mechanical Metamaterials\u201d, so remarkable. In this work, physicists Corentin Coulais (University of Amsterdam), Martin van Hecke (AMOLF and Leiden University), and Michael Czajkowski and D. Zeb Rocklin (Georgia Tech, USA), approach a highly-studied exotic elastic material, uncover an intuitive geometrical description of the pronounced, nonlinear \u2018soft\u2019 deformations, and show how to activate any of these deformations on-demand with minimal inputs.<\/p>\n\n\n\n A puppet is typically soft, from the physics perspective, as it is made with hinges and ball-in-socket joints, soft cloth, silicone, and flexible filaments. It is this maneuverability that makes the puppeteer\u2019s job possible: without flexibility, a puppet cannot dance. Puppet design is therefore much like the work of a researcher in mechanical metamaterials. Metamaterials \u2013 materials that are not found in nature but are constructed in the lab \u2013 similarly rely on the use of hinges, folds, cuts, and \u201cflexible\u201d ingredients to display a variety of counterintuitive physics. The diverse and unexpected possibilities of metamaterials have been steadily revealed over the past 10 years of intense research. Many of the new behaviors have emerged from the development of \u2018auxetics\u2019, materials that tend to shrink<\/em> in all directions when they are compressed, rather than expanding, as we are used to. The so-called \u201cRotating Squares\u201d metamaterial \u2013 see the animation below \u2013 is one of the most common and intuitive examples of this behavior. Although the Rotating Squares material is already one of the most heavily researched metamaterials, researchers are still able to uncover entirely new and powerful physics hiding within.<\/p>\n\n\n\n The new results that were now obtained rely on the observation that maximally auxetic metamaterials like the Rotating Squares material deform conformally<\/em>. Conformal deformation, put simply, means that any angle drawn on the material before and after deformation will look the same. This observation may seem mundane, but for mathematicians the conformal property can be very powerful in studying and describing a material\u2019s behaviour. Therefore, the researchers carefully showed that the deformations that arise from a set of arbitrary \u201cloadings\u201d on the material, including the foot pictured above, to a high degree of accuracy have the property of conformality.<\/p>\n\n\n\n This insight allows for a variety of theoretical advances in the description of the material. These advances culminated in a recipe to choose any of the conformal deformations of the whole material, and reverse engineer how to cause it by the manipulating boundary springs. These boundary springs are the \u201cstrings\u201d the puppeteer may use to influence the puppet, and by variably choosing the spring lengths, the overall shape of the material can be chosen from an infinite variety of possibilities.<\/p>\n\n\n\n