Lower bounds for the energy in a crumpled elastic sheet - A minimal ridge

Shankar C. Venkataramani

doi:10.1088/0951-7715/17/1/017

Lower bounds for the energy in a crumpled elastic sheet - A minimal ridge

Shankar C. Venkataramani

Research output: Contribution to journal › Article › peer-review

53 Scopus citations

Abstract

We study the linearized Föppl-von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2α. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness, σ, and the bending angle. We show that the minimum energy scales as σ^5/3σ^7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as σ.

Original language	English (US)
Pages (from-to)	301-312
Number of pages	12
Journal	Nonlinearity
Volume	17
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/17/1/017
State	Published - Jan 2004
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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AB - We study the linearized Föppl-von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2α. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness, σ, and the bending angle. We show that the minimum energy scales as σ5/3σ7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as σ.

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Lower bounds for the energy in a crumpled elastic sheet - A minimal ridge

Abstract

ASJC Scopus subject areas

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