Elasticity and Geometry: From Hair Curls to the Nonlinear Response of Shells

ISBN : 9780198506256

Basile Audoly; Yves Pomeau
600 Pages
175 x 249 mm
Pub date
Jun 2010
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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 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.


1. Introduction
2. Three-dimensional elasticity
3. Equations for elastic rods
4. Mechanics of the human hair
5. Rippled leaves, uncoiled springs
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
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

About the author: 

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

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