Defects and boundary layers in non-Euclidean plates

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the Föppl-von Kármán reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers - deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet.

Original languageEnglish (US)
Pages (from-to)3553-3581
Number of pages29
JournalNonlinearity
Volume25
Issue number12
DOIs
StatePublished - Dec 2012

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Boundary Layer
boundary layers
Boundary layers
Defects
annuli
Ring or annulus
defects
elastic sheets
curvature
Global Minimizer
Local Minimizer
Negative Curvature
Line
Scaling laws
Total curvature
saddles
Saddle
Scaling Laws
profiles
scaling laws

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Defects and boundary layers in non-Euclidean plates. / Gemmer, J. A.; Venkataramani, Shankar C.

In: Nonlinearity, Vol. 25, No. 12, 12.2012, p. 3553-3581.

Research output: Contribution to journalArticle

Gemmer, J. A. ; Venkataramani, Shankar C. / Defects and boundary layers in non-Euclidean plates. In: Nonlinearity. 2012 ; Vol. 25, No. 12. pp. 3553-3581.
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