Triangles that can more than hold their own

Kirigami will become more famous than origami if scientists keep up the current pace.

Late last year Cosmos described how US researchers used the principles of the Japanese art of paper folding and cutting to create materials that automatically reconfigure into new 2D and 3D structures in response to environmental stimuli.

And that was just the latest in a string of kirigami-inspired initiatives.

Now researchers from the US and the UK have produced these clever weight-bearing kirigami structures. Each raised triangle (shown above in close-up) is supported by neighbouring flaps (in blue) that work together to hold the structure in place without tape or adhesive.

The flaps are the novel bit, says Randall Kamien, from the University of Pennsylvania. They would normally be cut off.

However, graduate student Xinyu Wang “found that, in this particular geometry, you can get the flaps to fit”, he says.

While a single triangle wasn’t particularly strong on its own, Wang, Kamien and colleagues noticed that when several were arranged in a repetitive design, the force they could support was much greater than expected.

“Here was this structure that didn’t require tape, it had cuts, and it was really strong,” Kamien says. “Suddenly, we have this system that we hadn’t anticipated at all.”

To figure out what made this geometry so resilient, Wang made versions from different materials, including paper, copper and plastic, as well as versions where the flaps were taped, cut or damaged. 

Using industry-grade tension and compression testing equipment, the researchers found that the structure could support 14,000 times its own weight. The tilted, triangular design was strongest when the flaps were undamaged and untapped, they say, and also was stronger than the same design with vertical walls.

When the walls of the triangles are angled, Kamien adds, any force applied to the top can be translated into horizontal compression within the centre of the design. “With the vertical ones, there’s no way to turn a downward force into a sideways force without bending the paper,” he says. 

They also found that the paper-to-paper overlap from leaving the cut flaps in place allowed the triangles to press up against their neighbours, which helped distribute the vertical load.

“We figured out how to use materials that can bend and stretch, and we can actually strengthen these materials,” says Wang.

One possible application, she suggests, could be to make inexpensive, lightweight and deployable structures, such as temporary shelter tents that are strong and durable but can also be easily assembled and disassembled. It may also work for furniture.

The research is described in a paper in the journal Physical Review X.