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 have 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 multi-scale 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 team printed flat lattices that shape morph into a frequency-shifting antenna or the face of pioneering mathematician Carl Friedrich Gauss in response to a change in temperature. The research is published in the Proceedings of the National Academy of Sciences.
“Form both enables and constrains function,” said L Mahadevan, the 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 multi-scale geometry and multi-material printing to realize it, we are now able to build shape-shifting structures with the potential for a range of functions.”
“Together, we are creating new classes of shape-shifting matter,” said Jennifer A. Lewis, the Hansjorg Wyss Professor of Biologically Inspired Engineering at Harvard. “Using an integrated design and fabrication approach, we can encode complex ‘instruction sets’ within these printed materials that drive their shape-morphing behavior.”
4D print complex shape-shifting Gauss faces
To create complex and doubly-curved shapes — such as those found on a face — the team turned to a bilayer, multimaterial lattice design. The open cells of the curved lattice give it the ability to grow or shrink a lot, even if the material itself undergoes limited extension. To achieve complex curves, growing and shrinking the lattice on its own isn’t enough. You need to be able to direct the growth locally.
By printing materials with different thermal expansion behavior in pre-defined configurations, the researchers can control the growth and shrinkage of each individual rib of the lattice, which in turn gives rise to complex bending of the printed lattice both within and out of plane. The SEAS researchers used four different materials and programmed each rib of the lattice to change shape in response to a change in temperature. Using this method, they printed a shape-shifting patch antenna, which can change resonant frequencies as it changes shape.
To showcase the ability of the method to create a complex surface with multiscale curvature, the researchers decided to print a human face. They chose the face of the 19th-century mathematician who laid the foundations of differential geometry: Carl Friederich Gauss. The researchers began with a 2D portrait of Gauss, painted in 1840, and generated a 3D surface using an open-source artificial intelligence algorithm. They then programmed the ribs in the different layers of the lattice to grow and shrink, mapping the curves of Gauss’ face.
This inverse design approach and multimaterial 4D printing method could be extended to other stimuli-responsive materials and be used to create scalable, reversible, shape-shifting structures with unprecedented complexity. Application areas include, soft electronics, smart fabrics, tissue engineering, robotics and beyond.
“This work was enabled by recent advances in posing and solving geometric inverse problems combined with 4D-printing technologies using multiple materials. Going forward, our hope is that this multi-disciplinary approach for shaping matter will be broadly adopted,” said Mahadevan.
Co-first authors of the papers are Wim M. van Rees and J. William Boley. This research was co-authored by Charles Lissandrello, Mark Horenstein, Ryan Truby, and Arda Kotikian. It was supported by the National Science Foundation and Draper Laboratory. Harvard’s Office of Technology Development has protected the intellectual property related to this work, along with a broad portfolio of 3D printing technology from the Lewis Lab, and is currently exploring the commercialization opportunities.