Elasticité tridimensionnelle. (French) Zbl 0572.73027

Recherches en Mathématiques Appliquées, 1. Paris etc.: Masson. 168 p. (1986).
This textbook consists of two parts: an introduction to finite elasticity and, secondly, the existence theorems within the three-dimensional field theory.
The author starts with the description of the geometry of deformation with respect to reference configurations, the systems of forces, analysis of stress and the equations of equilibrium and equivalent variational expressions. The part of constitutive laws contains the well-known concepts of material indifference, isotropy, hyper-elasticity, and the representations of isotropic tensor functions. The second part treats the results of existence of the boundary value problems in elasticity: linearization, implicit function theorem, incremental semi-direct methods, classical convex analysis, up to J. Ball’s polyconvexity.
The exposition has a rigorous mathematical standard and surely is an interesting modern introduction.
Reviewer: A.Bertram


74B99 Elastic materials
74B20 Nonlinear elasticity
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74A20 Theory of constitutive functions in solid mechanics