Nonlinear Problems of Elasticity

This monograph, the second of the two volumes forming the third edition, is an enlarged, completely updated, and extensively revised version of the corresponding material from the authoritative second edition. It is completely self-contained.

This volume contains chapters on tensors, three-dimensional continuum mechanics, constitutive equations and their physically natural restrictions for three-dimensional elasticity and strain-rate viscoelasticity, steady-state and dynamical problems for these theories, general geometrically and mechanically exact theories of rods and shells, methods for treating dynamical problems of strain-rate viscoelasticity, and the role of material response for quasilinear hyperbolic systems of elasticity.

Each chapter contains a wealth of interesting, challenging, and tractable exercises.

From the reviews of the second edition:

"This second edition accounts for the developments since the first edition was published, and differs from the first edition in many points. The book has been reorganized and several parts have been added. The already impressive body of references has been further expanded. The reviewer highly recommends this book both to graduate students and to scholars interested in the theory of elasticity." (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2006e:74001)
"The second extended edition of the reviewed monograph gives a fundamental presentation of problems of nonlinear elasticity. Every chapter is equipped by instructive exercises, unsolved problems and exhaustive historical comments. The book could be very useful to applied mathematicians and engineers using in their works the elasticity theory and to specialists dealing with applications of differential equations and bifurcation theory." (Boris V. Loginov, Zentralblatt MATH, Vol. 1098 (24), 2006)
"Antman's impressive work is a comprehensivetreatise on nonlinear elasticity and a quintessential example of applied nonlinear analysis. The text has been revised and updated, Several new sections have been added This book is a 'must' for researchers and graduate students interested in nonlinear continuum mechanics and applied analysis. The work is scholarly and well written. 'This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems.'" (Timothy J. Healey, SIAM Review, Vol. 49 (2), 2007)

Highlights the mathematical tools of nonlinear analysis through self-contained presentations Suitable for mathematicians and industry professionals studying nonlinear elasticity Includes supplementary material & chapter-level exercises

Contenu
Background.- The Equations of Motion for Extensible Strings.- Elementary Problems for Elastic Strings.- Planar Steady-State Problems for Elastic Rods.- to Bifurcation Theory and its Applications to Elasticity.- Global Bifurcation Problems for Strings and Rods.- Variational Methods.- Theory of Rods Deforming in Space.- Spatial Problems for Rods.- Axisymmetric Equilibria of Shells.- Tensors.- 3-Dimensional Continuum Mechanics.- 3-Dimensional Theory of Nonlinear Elasticity.- Problems in Nonlinear Elasticity.- Large-Strain Plasticity.- General Theories of Rods.- General Theories of Shells.- Dynamical Problems.- Appendix. Topics in Linear Analysis.- Appendix. Local Nonlinear Analysis.- Appendix. Degree Theory.