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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010275287 | TA418 A93 2010 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Author Notes
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.
Reviews 1
Choice Review
Nonlinearities that complicate the mathematics of elasticity arise either from large displacements that cause geometrical distortions, or from large strains that cause deviations from Hooke's law. Civil engineers traditionally study elasticity to determine the structural integrity of load-bearing structures, and thus assume small displacements (because usually they want to know whether, not how, something will collapse) and small strains. Here, Audoly and Pomeau (both, CNRS, France) cover recent advances in nonlinear mathematics serving the demands of new applications--particularly from biophysics and biomechanics, but computer graphics also. Though the authors carry forward the assumption of small strains, the novelty lies in tackling large displacement-type geometrical nonlinearities by making new connections to differential geometry and the calculus of variations. The "hair curls" of the title provide an example of rods with intrinsic curvature opposing gravity; chapter 4 treats this model with realism sufficient for computer-simulated hairstyles (though interstrand interactions remain intractable). Chapter 9, "Crumpled Paper" (flat elastic plates with fixed intrinsic geometry that exhibit polyhedral networks), also shows this sophisticated mathematics, giving insight into familiar objects of daily life. The book's separate sections ("Rods," "Plates," and "Shells"), designed to stand on their own, make for repetitive straight reading. Summing Up: Recommended. Upper-division undergraduates through professionals. D. V. Feldman University of New Hampshire
