Two disks with the face of Max Planck marked out on their surfaces

Shapeshifting growth rules from nature inspire method for engineering new shapes

Image credit: Harvard SEAS

Harvard University engineers have looked to nature in order to develop a mathematical technique to grow any shape from any starting shape.

Over billions of years of natural selection, plants and animals have developed the ability to change their shape as they grow: from an acorn to a tree, or frogspawn to a frog. This ability to shapeshift is based around a set of basic growth rules.

“Architect Louis Sullivan once said that ‘form ever follows function’,” said Professor Lahshminarayanan Mahadevan, senior author of the Harvard study, who had previously led research into how naturally shapeshifting organisms control their transformations. “But if one took the opposite perspective - that perhaps function should follow form - how can we inverse design form?”

The idea of this is to understand these growth rules and grasp the ability to shift objects into almost any target shape imaginable from any starting shape. Already, engineers have developed simple machines capable of changing their shape with little human input, such as “shapeshifting pasta” and a simple robot which folds exoskeletons for different purposes, although these examples tend to be limited to a small number of forms.

Inspired by the development of leaves from buds, the researchers, from the John A Paulson School of Engineering and Applied Sciences and the Wyss Institute for Biologically Inspired Engineering, went back to basics and developed a mathematical theory to describe this mysterious transformation.

This theory also describes how to pattern two layers of elastic materials glued together which respond differently (swelling in different directions or to different extents) to an external stimuli.

“We found a very elegant relationship in a material that consists of these two layers,” said Wim van Rees, a PhD student and first author of the study. “You can take the growth of a bilayer and write its energy directly in terms of a curved [single] layer.”

This allows for the creation of almost any shape from a basic, programmable shell, as long as you know the curvature of the desired shape. The researchers demonstrated that this approach works in practice by modelling the growth of a snapdragon petal from a cylinder, a textured map of the Colorado River basin from a sheet and the face of physicist Max Planck from a disc.

“Overall, our research combines our knowledge of the geometry and physics of slender shells with new mathematical algorithms and computations to create design rules for engineering shape,” said Professor Mahadevan.

“It paves the way for manufacturing advances in 4D printing of shapeshifting optical and mechanical elements, soft robotics, as well as tissue engineering.”

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