Ciarlet P.G. Mathematical Elasticity. Volume 1. Three-dimensional Elasticity

Elsevier Science B.V., 1988. — 465 p. — (Studies in Mathematics and its Applications, Vol. 20). — ISBN: 0444702598, 9780444702593.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.Description of three-dimensional elasticity
Geometrical and other preliminaries
The equations of equilibrium and the principle of virtual work
Elastic materials and their constitutive equations
Hyperelasticity
The boundary value problems of three-dimensional elasticity
Mathematical methods in three-dimensional elasticity
Existence theory based on the implicit function theorem
Existence theory based on the minimization of the energy