Scientists and engineers have recently tapped the paper-folding arts of origami and kirigami, which also allows cutting, to transform flat surfaces into three-dimensional structures. The techniques yield stretchable, lightweight, transformable structures that can be used in electronics, mechanical parts, and robots.

Most kirigami designs so far have relied on simple parallel cuts. By perforating thin plastic sheets with an orthogonal pattern and stretching them in different directions, researchers at Harvard University have now been able to make them pop up into unique three-dimensional (3D) shapes made of regular arrangements of mountains and valleys.

When the stretch is released, the flexible plastic sheet pops back to its original flat form. But if it is stretched enough, the folds become permanent, professor of natural sciences Katia Bertoldi and her post-doctoral fellow Ahmad Rafsanjani found. And by changing the stretching direction, they can tune its mechanical properties.

In an article published in a recent issue of Physical Review Letters, the duo reports different cubic-patterned kirigami structures made from flat sheets using their technique. Some structures can be folded flat, while others can be bent into a saddle shape or twisted (see video). One structure was demonstrated to carry a weight of 20 grams without sagging, while the flat sheet it is made from collapses under the weight.

Many scientists have recently combined paper art principles with sophisticated computer algorithms to create flat materials that are pre-programmed to morph into complex, reconfigurable shapes. Kirigami is especially practical because it does not require pre-creased folds but rather depends on the buckling in a flat sheet that has been pre-cut with a laser. Stretching induces buckling, which makes the sheet pop up into a 3D pattern determined by the cuts. Researchers have used kirigami to make shape-changing materials, stretchable batteries, and sun-tracking solar cells.

Bertoldi and Rafsanjani used a laser cutter to perforate plastic sheets with a square array of cuts that are at right angles to each other (see Figure). This leaves a network of squares connected by small ligaments. This well-known pattern has been studied for decades, Rafsanjani says, but he and Bertoldi tried to “figure out what happens when the sheet is very thin. When you reduce thickness, there’s instability and buckling. You can play with loading direction.” That is, the direction in which the sheet is pulled. Depending on the angle to the cuts, the pulling direction leads to a different final 3D shape. The researchers plan to use the technique to develop materials that can offer tunable friction properties.

“The advance here is the design of a specific mechanism to create three-dimensional targets, says Randall Kamien, a physicist at the University of Pennsylvania who works in this area. “There is always a problem with degeneracy in folding. They have used mechanical bias to control the curvature and break the degeneracy.”

Read the abstract in Physical Review Letters.