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Geometry and Anomalous Dynamic Growth of Elastic instabiliTies

Periodic Reporting for period 3 - GADGET (Geometry and Anomalous Dynamic Growth of Elastic instabiliTies)

Reporting period: 2018-04-01 to 2019-09-30

Elastic instabilities are ubiquitous, from the wrinkles that form on skin to the ‘snap-through’ of an umbrella on a windy day. The complex patterns such instabilities make, and the great speed with which they develop, have led to a host of technological and scientific applications. However, recent experiments have revealed significant gaps in our theoretical understanding of such instabilities, particularly in the roles played by geometry and dynamics. I will establish a group to develop and validate a theoretical framework within which these results can be understood. Central to my approach is an appreciation of the crucial role of geometry in the pattern formation and dynamics of elastic instabilities.

As a starting point, I will consider the model problem of a pressurized elastic shell subject to a geometrically large deformation. This system develops either wrinkles or a stress-focusing instability depending on the internal pressure. As such, this is a natural paradigm with which to understand geometrical features of deformation relevant across length scales from deformed viruses to the subduction zones in Earth’s tectonic plates. My team will combine theoretical and computational approaches with tabletop experiments to determine a new set of shell deformations that are generically observed in contradiction of the classic ‘mirror buckling’. Understanding why these new shapes emerge will transform our perception of shell instabilities and provide new fundamental building blocks with which to model them. These ideas will also be used to transform our understanding of a number of other, previously mysterious, elastic instabilities of practical interest. Turning our focus to the dynamics of instabilities such as the snap-through of shells, we will show that accounting for geometry is again crucial. The new insight gained through this project will increase our ability to control elastic instabilities, benefitting a range of technological and scientific applications.
We have developed a number of new theoretical insights into elastic instabilities including:

A quantitative understanding of the dynamics of elastic snap-through. This demonstrated that snap-through may be subject to a critical slowing down, potentially explaining why previous experiments have observed anomalously slow dynamic snap-through.

An understanding of the spatially varying wrinkle patterns observed in a number of static experiments.
In the remainder of the project, we will continue to work on dynamic instabilities, focusing on how pattern selection occurs in dynamics systems.
Dynamic wrinkling of a thin sheet induced by impact