Elasticity and Geometry: From hair curls to the nonlinear response of shells

Hardcover | August 18, 2010

byBasile Audoly, Yves Pomeau

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We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in ping-pong or soccer. The theory of elasticity is essential to the recent developments of applied andfundamental science, such as the bio-mechanics of DNA filaments and other macro-molecules, and the animation of virtual characters in computer graphics and materials science. In this book, the emphasis is on the elasticity of thin bodies (plates, shells, rods) in connection with geometry. It coverssuch topics as the mechanics of hairs (curled and straight), the buckling instabilities of stressed plates, including folds and conical points appearing at larger stresses, the geometric rigidity of elastic shells, and the delamination of thin compressed films. It applies general methods ofclassical analysis, including advanced nonlinear aspects (bifurcation theory, boundary layer analysis), to derive detailed, fully explicit solutions to specific problems. These theoretical concepts are discussed in connection with experiments. The book is self-contained. Mathematical prerequisitesare vector analysis and differential equations. The book can serve as a concrete introduction to nonlinear methods in analysis.

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We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in ping-pong or soccer. The theory of elasticity is essential to the recent developments of applied andfundamental science, such as the bio-mechanics of...

Dr. Basile Audoly is Research Fellow at CNRS Paris. Professor Yves Pomeau is Senior Researcher at CNRS and Professor of Mathematics at the University of Arizona.

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Kobo ebook|Nov 9 2012

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Format:HardcoverDimensions:600 pages, 9.69 × 6.73 × 0.01 inPublished:August 18, 2010Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198506252

ISBN - 13:9780198506256

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Table of Contents

1. Introduction2. Three-dimensional elasticityI: RODS3. Equations for elastic rods4. Mechanics of the human hair5. Rippled leaves, uncoiled springsII: PLATES6. The equations for elastic plates7. End effects in plate buckling8. Finite amplitude buckling of a strip9. Crumpled paper10. Fractal buckling near edgesIII: SHELLS11. Geometric rigidity of surfaces12. Shells of revolution13. The elastic torus14. Spherical shell pushed by a wallAppendix A: Calculus of variations: a worked exampleAppendix B: Boundary and interior layersAppendix C: The geometry of helicesAppendix D: Derivation of the plate equations by formal expansion from 3D elasticity

Editorial Reviews

"A most welcome addition to the literature with a refreshingly new approach, first in that it discusses in depth how the differential geometry of surfaces is connected with the theory of elastic plates and shells, second in that, as a consequence of this perspective, it sheds new light andunderstanding on practical problems." --Philippe Ciarlet, City University of Hong Kong