Three-Dimensional Elasticity, Volume 20

This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Part A. Description of Three-Dimensional Elasticity 1. Geometrical and other preliminaries. 2. The equations of equilibrium and the principle of virtual work. 3. Elastic materials and their constitutive equations. 4. Hyperelasticity. 5. The boundary value problems of three-dimensional elasticity. Part B. Mathematical Methods in Three-Dimensional Elasticity 6. Existence theory based on the implicit function theorem. 7. Existence theory based on the minimization of the Energy. Bibliography. Index.