SIAM News Blog

Botanical Structures Inspire Innovative 4D Printing Method

By Lina Sorg

Nature is wrought with patterns and complex routines. Spirals, tessellations, waves, and various types of symmetry frequently appear in natural forms. The microstructures and tissue composition of plants and flowers allow them to continuously adjust to their environment. Organs such as tendrils and leaves undergo numerous shape changes, depending on stimuli like temperature, humidity, and light. Sometimes, these patterns and routines find function in mathematics.

A team of researchers at Harvard University is currently utilizing nature’s behavior in a novel application. Drawing inspiration from the way plants alter their form and adapt to changing conditions, scientists at the Wyss Institute for Biologically Inspired Engineering at Harvard University and the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have expanded microscale 3D printing. By incorporating the fourth dimension of time, they designed hydrogel composite structures – printed with 4D technology – that change shape when submerged in water.

The researchers developed a proprietary model that combines techniques of both mathematics and materials science. The model calculates necessary printing pathways and predicts how a 4D object must be generated to attain the intended shape-shifting response. By doing so, it solves the so-called “inverse problem,” the challenge of predicting the printing toolpath to encode detailed swelling behaviors that result in the desired shape. The team then reverse-engineered the problem, learning to control the spacing and direction of the ink filaments to further refine the printed shapes. Read more about the process here.

The ink used for the hydrogel composites prints in a single step. It contains aligned cellulose fibrils, which come from wood and allow for anisotropic swelling. These fibrils are anisotropic, meaning they are directionally-dependent and thus evoke various directional properties that can then be controlled or predicted. Therefore, the ink can be programmed to construct complex shape changes in various conditions. The ink flows smoothly through the printhead, but hardens quickly upon printing. Its composition is flexible, in that different types of hydrogel materials cause varying stimuli-responsive behavior. Anisotropic fillers can also replace the cellulose fibrils for modified results. When submerged in water, the ink swells differentially along or perpendicular to the printing path.

According to senior author Jennifer Lewis, the hydrogel composite structures signify a significant development in programmable materials. The success of the researchers’ mathematical model paves the way for future 4D printing opportunities, including applications in soft electronics, tissue engineering, smart textiles, and biomedical devices.

A paper about the printing process recently published in Nature Materials.

Lina Sorg is associate editor of SIAM News.
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