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The Formation of Singularities in Non-Euclidean Plates

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abstract
In the non-Euclidean model of elasticity, growth is modeled by a Riemannian metric that encodes local changes in distance. In response to the growth, the sheet deforms to minimize an elastic energy. The elastic energy consists of the sum of the stretching and bending energy. Minimizers of the stretching energy consist of isometric immersions of the metric, while minimizers of the bending energy remain flat. The competition between bending and stretching selects a pattern in the sheet. In this thesis, we show that periodic patterns naturally arise as low energy deformations of the sheet. We do this by explicitly constructing isometric immersions in the small slopes regime for algebraic and exponentially decaying metrics. Our results are obtained using a priori analysis as well as through rigorous justification using Γ-convergence methods. Qualitatively, our results agree with patterns observed in thin elastic sheets.
subject
contributor
Rezek, Maximilian (author)
Gemmer, John (committee chair)
Rouse, Jeremy (committee member)
date
2019-05-24T08:35:46Z (accessioned)
2019-05-24T08:35:46Z (available)
2019 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/93960 (uri)
language
en (iso)
publisher
Wake Forest University
title
The Formation of Singularities in Non-Euclidean Plates
type
Thesis

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