Elasticity and Geometry: From hair curls to the non-linear response of shells

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Basile Audoly (, CNRS and Université Pierre et Marie Curie, Paris VI, France) Yves Pomeau (, CNRS, École Normale Supérieure, Paris, and University of Arizona, Tucson, USA)

Elasticity and Geometry

From hair curls to the non-linear response of shells

Basile Audoly (, CNRS and Université Pierre et Marie Curie, Paris VI, France), Yves Pomeau (, CNRS, École Normale Supérieure, Paris, and University of Arizona, Tucson, USA)

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English

Oxford University Press
01 July 2010

Biomechanics, human kinetics; Geometry; Applied mathematics; Physics; Classical mechanics; Mechanical engineering & materials

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 and fundamental 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 covers such 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 of classical 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 prerequisites are vector analysis and differential equations. The book can serve as a concrete introduction to nonlinear methods in analysis.

By: Basile Audoly ( CNRS and Université Pierre et Marie Curie Paris VI France), Yves Pomeau (, CNRS, École Normale Supérieure, Paris, and University of Arizona, Tucson, USA)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 249mm, Width: 175mm, Spine: 36mm
Weight: 1.313kg
ISBN: 9780198506256
ISBN 10: 0198506252
Pages: 598
Publication Date: 01 July 2010
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1: Introduction 2: Three-dimensional elasticity I: RODS 3: Equations for elastic rods 4: Mechanics of the human hair 5: Rippled leaves, uncoiled springs II: PLATES 6: The equations for elastic plates 7: End effects in plate buckling 8: Finite amplitude buckling of a strip 9: Crumpled paper 10: Fractal buckling near edges III: SHELLS 11: Geometric rigidity of surfaces 12: Shells of revolution 13: The elastic torus 14: Spherical shell pushed by a wall Appendix A: Calculus of variations: a worked example Appendix B: Boundary and interior layers Appendix C: The geometry of helices Appendix D: Derivation of the plate equations by formal expansion from 3D elasticity

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

Reviews for Elasticity and Geometry: From hair curls to the non-linear response of shells

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 and understanding on practical problems. * Philippe Ciarlet, City University of Hong Kong *