What would it take to transform a flat sheet into a human face? How would the sheet need to grow and shrink to form eyes that are concave, a nose that’s convex, and a chin that protrudes?
How to encode and release complex curves in shape-shifting structures is at the center of research led by the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) and the Harvard Wyss Institute of Biologically Inspired Engineering.
Over the past decade, theorists and experimentalists have found inspiration in nature as they sought to unravel the physics, build mathematical frameworks, and develop materials and 3D- and 4D-printing techniques for structures that can change shape in response to external stimuli.
However, complex multiscale curvature has remained out of reach.
Now, researchers have created the most complex shape-shifting structures to date — lattices composed of multiple materials that grow or shrink in response to changes in temperature. To demonstrate their technique, the research team printed flat lattices that morph into a frequency-shifting antenna or the face of pioneering mathematician Carl Friedrich Gauss.
The research is published in the Proceedings of the National Academy of Sciences.
“Form both enables and constrains function,” said L Mahadevan, the Lola England de Valpine Professor of Applied Mathematics and professor of physics and organismic and evolutionary biology at Harvard. “Using mathematics and computation to design form, and a combination of multiscale geometry and multimaterial printing to realize it, we are now able to build shape-shifting structures with the potential for a range of functions.”