Mathematicians develop new method for creating transformable kirigami structures

Kirigami, a Japanese paper craft, has taken pop-up books to a new level by transforming two-dimensional sheets into intricate, three-dimensional structures. Inspired by this art form, scientists and engineers have applied kirigami principles to design a range of innovative devices and materials, including robotic grippers, stretchable electronics, and shape-shifting materials. However, until now, there was no blueprint or computational strategy to determine the pattern of cuts necessary to achieve a specific transformation. A recent study published in Nature Computational Science introduces a general computational strategy for solving any two-dimensional kirigami-inspired transformation.

The researchers behind the study, affiliated with MIT, Harvard University, and Optiver, designed and fabricated various transformable kirigami structures using their new method. For example, they successfully transformed a square shape into a circle shape—a task previously considered mathematically impossible. This breakthrough has significant implications for engineering design problems. The computational strategy could be used to develop robots that can change shape to perform specific tasks or navigate challenging environments. It also holds promise for designing active materials, such as adaptive coverings for buildings and homes.

The research team’s work builds on their previous investigations into kirigami and origami, identifying mathematical connections between the two art forms. They developed an optimization approach for kirigami in 2019, but it was computationally intensive and time-consuming. In 2021, they took a different perspective and derived a more efficient strategy for origami design. Drawing inspiration from this approach, the researchers sought to apply a similar method to kirigami. By focusing on the empty spaces created between cuts and their relationships to each other, they devised a formula for efficient kirigami design. The team studied interconnected quadrilateral tiles and analyzed the changes in empty spaces as the tiles were manipulated. Through their formula, they determined the angle and length of cuts required to transform a two-dimensional sheet from one shape to another.

To physically realize their designs, the researchers faced the challenge of finding suitable materials for the tile-connecting hinges. They discovered that fabric, which is strong in tension and tear-resistant while allowing for zero bending radius, served as an ideal hinge material. Using 3D printing and mold casting techniques, they embedded fabric strips into plastic tiles, enabling them to bend against each other. With these fabrication methods, the team successfully created circle-shaped mosaics that transformed into squares and simple triangle mosaics that morphed into more complex heart shapes. They demonstrated that their mathematical formulation guarantees the ability to transform any two-dimensional shape and are now looking to extend their approach to 3D kirigami.

Overall, this study presents a groundbreaking computational strategy for solving kirigami-inspired transformations, offering engineers a powerful tool to design various shape-changing devices and materials. The potential applications range from robotics to adaptive architecture, opening up exciting possibilities for the future of engineering and design.

Source: Massachusetts Institute of Technology

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