The University of Arizona
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Principles of Pattern Formation for Confined Elastic Shells

[CANCELLED] Analysis, Dynamics, and Applications Seminar

Principles of Pattern Formation for Confined Elastic Shells
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Ian Tobasco, Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago

Dried fruits wrinkle for the same reason that leaves and flowers do — mechanical instabilities arising due to a naturally occurring mismatch in lengths. Can such geometric incompatibilities be used for the rational design and control of wrinkle patterns at will? In this talk, we discuss the possibility of designing wrinkle patterns "in the large" using a recently derived effective or coarse-grained model for wrinkles arising in the vanishing thickness limit. After explaining the basic mechanics involved, we show how the model predicts the patterns in various experiments and simulations of thin and ultrathin confined elastic shells. More generally, we derive a classification scheme for wrinkle patterns into three basic types, as well as a Plateau-like principle predicting the arrangement of wrinkles in the negatively-curved (saddle-shaped) case. Such rules open the way towards the principled design of wrinkle patterns, with potential applications ranging from flexible electronics to synthetic skins. 

This is joint work with Yousra Timounay and Eleni Katifori (UPenn), and Desislava Todorova and Joseph D. Paulsen (Syracuse).