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New insights into elastic instabilities

Research sheds new light on the role geometry plays in causing elastic instabilities.

Fundamental Research

Elastic instability is the name given to the instabilities that occur in elastic systems. Although this might sound like an overly complex scientific theory, in fact, elastic instabilities can be found everywhere – from the wrinkles that form on your skin to the ‘snap-through’ of an umbrella on a windy day. Despite the amount of work that has gone into studying these instabilities, there are still significant gaps in our theoretical understanding of them. The EU-funded GADGET project aims to fill one of the most glaring gaps, namely, the intertwined roles played by geometry and dynamics. “This project sought to understand how elastic instabilities take place and, specifically, show how geometry is an important ingredient in both causing such instabilities and determining how fast they take place,” says Dominic Vella, a professor of applied mathematics at the University of Oxford’s Mathematical Institute.

The role of geometry

Vella, who served as the GADGET project coordinator, has spent his career studying the various aspects of solid and fluid mechanics, with a particular focus on the wrinkling of thin elastic objects and surface tension effects. In this European Research Council supported project, he was able to establish the crucial role of geometry in pattern formation and the dynamics of elastic instabilities. One of the project’s key findings was that the geometry of an object can cause snap-through to be surprisingly slow. “It had been thought that some of the slow snaps observed experimentally were anomalous and perhaps caused by some non-trivial material behaviour,” explains Vella. “Our research showed that in fact geometry alone can have a similar effect and that this geometric origin makes it a generic feature of such systems.” Another important outcome was a demonstration of how the wrinkling of objects can give rise to a new class of shapes that objects can adopt, which Vella calls ‘wrinkly isometries’. “These findings represent a step change in our understanding of how the mathematical structure of elastic instabilities can be both intellectually interesting as well as technologically useful,” adds Vella.

Looking to the future

According to Vella, the work done during the GADGET project has opened the door to new research and opportunities within the field of elastic systems. “Our team included two PhD students and four post-doctoral students,” he notes. “I’m excited to see how the experience and training they gained during this project will set them up for fulfilling scientific careers.” Although the GADGET project is now finished, Vella’s work continues. “The next step is to try to understand whether we can convert the insights gained during this project into methods for controlling the dynamics of instability,” Vella concludes. “For example, whether or not we can use our enhanced understanding of how and why things sometimes move slowly to control elements in soft robots – this is the type of work that lies ahead.”

Keywords

GADGET, elastic instabilities, elastic systems, geometry, mathematics

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