La struttura degli origami 31.10.17

Lo studio delle pieghe degli origami immaginati come atomi in un reticolo sta aiutando i ricercatori a scoprire i comportamenti complessi e strani nascosti in strutture semplici.

In 1970, an astrophysicist named Koryo Miura conceived what would become one of the most well-known and well-studied folds in origami: the Miura-ori. The pattern of creases forms a tessellation of parallelograms, and the whole structure collapses and unfolds in a single motion — providing an elegant way to fold a map. It also proved an efficient way to pack a solar panel for a spacecraft, an idea Miura proposed in 1985 and then launched into reality on Japan's Space Flyer Unit satellite in 1995.

Back on Earth, the Miura-ori has continued to find more uses. The fold imbues a floppy sheet with form and stiffness, making it a promising metamaterial — a material whose properties depend not on its composition but on its structure. The Miura-ori is also unique in having what's called a negative Poisson's ratio. When you push on its sides, the top and bottom will contract. But that's not the case for most objects. Try squeezing a banana, for example, and a mess will squirt out from its ends.

Researchers have explored how to use Miura-ori to build tubes, curves and other structures, which they say could have applications in robotics, aerospace and architecture. Even fashion designers have been inspired to incorporate Miura-ori into dresses and scarves.

Now Michael Assis, a physicist at the University of Newcastle in Australia, is taking a seemingly unusual approach to understanding Miura-ori and related folds: by viewing them through the lens of statistical mechanics.

Assis' new analysis, which is under review at Physical Review E, is the first to use statistical mechanics to describe a true origami pattern. The work is also the first to model origami using a pencil-and-paper approach that produces exact solutions — calculations that don’t rely on approximations or numerical computation.