“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.” Lewis is also a core faculty member of the Wyss Institute.

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,” said co-first author Wim M. van Rees, who was a postdoctoral fellow at SEAS and is now an assistant professor at MIT.

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.

“That’s where the materials palette that we’ve developed comes in,” said J. William Boley, a former postdoctoral fellow at SEAS and co-first author of the paper. “By printing materials with different thermal expansion behavior in predefined configurations, we 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.” Boley is now an assistant professor at Boston University.

The 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 that of the 19th-century mathematician who laid the foundations of differential geometry: Carl Friedrich Gauss. They 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 used to create scalable, reversible, shape-shifting structures with unprecedented complexity.

“Application areas include soft electronics, smart fabrics, tissue engineering, robotics, and beyond,” said Boley.

“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 multidisciplinary approach for shaping matter will be broadly adopted,” said Mahadevan.

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.