A March 16, 2016 article by Jonathan Webb for BBC (British Broadcasting Corporation) News Online describes research on metamaterials from McGill University (Montréal, Canada),

Metamaterials are engineered to have properties that don’t occur naturally, such as getting wider when stretched instead of just longer and thinner.

These perforated rubber sheets made by a Canadian team do just that – and then remain stable in their expanded state until they are squeezed back again.

Such designs could help make expandable stents or spacecraft components.

“In conventional materials, when you pull in one direction it will contract in other directions,” said Dr Ahmad Rafsanjani, from McGill University in Montreal.

“But with ‘auxetic’ materials, due to their internal architecture, when you pull in one direction they expand in the lateral direction.”

A March 16, 2016 article by Shannon Hall in the New Scientist provides more details,

This property comes from their geometric substructure, which when stationary looks like a series of connected squares. When the squares turn relative to each other, however, the material’s density lowers but its thickness increases, allowing it to grow when stretched.

But this twisting means that the materials lose their original shape as they expand. So Ahmad Rafsanjani and Damiano Pasini of McGill University in Montreal, Canada, set out to create a material that would grow when stretched yet keep its form.

To do this, they turned to a beautiful kind of geometry.

“There is a huge library of geometries when you look at Islamic architectures,” says Rafsanjani. The team picked their design from the walls of the Kharraqan towers, two mausoleums built in 1067 and 1093 in the plains in northern Iran.

Both Webb’s and Hall’s articles are embedded with images of the architecture. There’s also a New Scientist video demonstrating stretchability,

The researchers discussed this work in a presentation titled:  Multistable Compliant Auxetic Metamaterials Inspired by Geometric Patterns in Islamic Arts at the American Physical Society’s March 2016 meeting (March 14 – 18, 2016).