Nav: Home

Shaping animal, vegetable and mineral

October 16, 2017

Nature has a way of making complex shapes from a set of simple growth rules. The curve of a petal, the swoop of a branch, even the contours of our face are shaped by these processes. What if we could unlock those rules and reverse engineer nature's ability to grow an infinitely diverse array of shapes?

Scientists from the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have done just that. In a paper published in the Proceedings of the National Academy of Sciences, a team of researchers from SEAS and the Wyss Institute for Biologically Inspired Engineering demonstrate a technique to grow any target shape from any starting shape.

"Architect Louis Sullivan once said that 'form ever follows function'," said L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary Biology and of Physics and senior author of the study. "But if one took the opposite perspective, that perhaps function should follow form, how can we inverse design form?"

In previous research, the Mahadevan group used experiments and theory to explain how naturally morphing structures -- such as Venus flytraps, pine cones and flowers -- changed their shape in the hopes of one day being able to control and mimic these natural processes. And indeed, experimentalists have begun to harness the power of simple, bioinspired growth patterns. For example, in 2016, in a collaboration with the group of Jennifer Lewis, the Hansjorg Wyss Professor of Biologically Inspired Engineering at SEAS and Core Faculty Member of the Wyss Institute, the team printed a range of structures that changed its shape over time in response to environmental stimuli.

"The challenge was how to do the inverse problem," said Wim van Rees, a postdoctoral fellow at SEAS and first author of the paper. "There's a lot of research on the experimental side but there's not enough on the theoretical side to explain what's actually happening. The question is, if I want to end with a specific shape, how do I design my initial structure?"

Inspired by the growth of leaves, the researchers developed a theory for how to pattern the growth orientations and magnitudes of a bilayer, two different layers of elastic materials glued together that respond differently to the same stimuli. By programming one layer to swell more and/or in a different direction than the other, the overall shape and curvature of the bilayer can be fully controlled. In principle, the bilayer can be made of any material, in any shape, and respond to any stimuli from heat to light, swelling, or even biological growth.

The team unraveled the mathematical connection between the behavior of the bilayer and that of a single layer.

"We found a very elegant relationship in a material that consists of these two layers," said van Rees. "You can take the growth of a bilayer and write its energy directly in terms of a curved monolayer."

That means that if you know the curvatures of any shape you can reverse engineer the energy and growth patterns needed to grow that shape using a bilayer.

"This kind of reverse engineering problem is notoriously difficult to solve, even using days of computation on a supercomputer," said Etienne Vouga, former postdoctoral fellow in the group, now an Assistant Professor of Computer Science at the University of Texas at Austin. "By elucidating how the physics and geometry of bilayers are intimately coupled, we were able to construct an algorithm that solves for the needed growth pattern in seconds, even on a laptop, no matter how complicated the target shape."

The researchers demonstrated the system by modeling the growth of a snapdragon flower petal from a cylinder, a topographical map of the Colorado river basin from a flat sheet and, most strikingly, the face of Max Planck, one of the founders of quantum physics, from a disk.

"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 Mahadevan. "It paves the way for manufacturing advances in 4-D printing of shape-shifting optical and mechanical elements, soft robotics as well as tissue engineering."
-end-
The researchers are already collaborating with experimentalists to try out some of these ideas.

This research was funded in part by the Swiss National Science Foundation and the US National Science Foundation.

Harvard John A. Paulson School of Engineering and Applied Sciences

Related Engineering Articles:

Engineering the meniscus
Damage to the meniscus is common, but there remains an unmet need for improved restorative therapies that can overcome poor healing in the avascular regions.
Artificially engineering the intestine
Short bowel syndrome is a debilitating condition with few treatment options, and these treatments have limited efficacy.
Reverse engineering the fireworks of life
An interdisciplinary team of Princeton researchers has successfully reverse engineered the components and sequence of events that lead to microtubule branching.
New method for engineering metabolic pathways
Two approaches provide a faster way to create enzymes and analyze their reactions, leading to the design of more complex molecules.
Engineering for high-speed devices
A research team from the University of Delaware has developed cutting-edge technology for photonics devices that could enable faster communications between phones and computers.
Breakthrough in blood vessel engineering
Growing functional blood vessel networks is no easy task. Previously, other groups have made networks that span millimeters in size.
Next-gen batteries possible with new engineering approach
Dramatically longer-lasting, faster-charging and safer lithium metal batteries may be possible, according to Penn State research, recently published in Nature Energy.
What can snakes teach us about engineering friction?
If you want to know how to make a sneaker with better traction, just ask a snake.
Engineering a plastic-eating enzyme
Scientists have engineered an enzyme which can digest some of our most commonly polluting plastics, providing a potential solution to one of the world's biggest environmental problems.
A new way to do metabolic engineering
University of Illinois researchers have created a novel metabolic engineering method that combines transcriptional activation, transcriptional interference, and gene deletion, and executes them simultaneously, making the process faster and easier.
More Engineering News and Engineering Current Events

Top Science Podcasts

We have hand picked the top science podcasts of 2019.
Now Playing: TED Radio Hour

Accessing Better Health
Essential health care is a right, not a privilege ... or is it? This hour, TED speakers explore how we can give everyone access to a healthier way of life, despite who you are or where you live. Guests include physician Raj Panjabi, former NYC health commissioner Mary Bassett, researcher Michael Hendryx, and neuroscientist Rachel Wurzman.
Now Playing: Science for the People

#544 Prosperity Without Growth
The societies we live in are organised around growth, objects, and driving forward a constantly expanding economy as benchmarks of success and prosperity. But this growing consumption at all costs is at odds with our understanding of what our planet can support. How do we lower the environmental impact of economic activity? How do we redefine success and prosperity separate from GDP, which politicians and governments have focused on for decades? We speak with ecological economist Tim Jackson, Professor of Sustainable Development at the University of Surrey, Director of the Centre for the Understanding of Sustainable Propserity, and author of...
Now Playing: Radiolab

An Announcement from Radiolab