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