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Nonlinear theory of elasticity. Transl. from the Russian by K. A. Lurie. (English) Zbl 0715.73017
North-Holland Series in Applied Mathematics and Mechanics, 36. Amsterdam etc.: North-Holland. xiv, 617 p. $ 168.50; Dfl. 295.00 (1990).
This monograph is the translation of the Russian original, which appeared in 1980 (Zbl 0506.73018), shortly after the death of the author. So it might be considered as a testimony of a long life of intensive scientific production. Indeed, the 600 pages contain a huge amount of information on the subject, carefully collected and translated in a homogeneous language, namely that of direct tensor notation “without reference to component representations which hinder the perception of basic concepts and operation with them” (A.I.L.). D’accord!
In comparison with other books in the field of finite elasticity, e.g., the excellent book “Introduction to rational elasticity” by C. C. Wang and C. Truesdell (1973; Zbl 0308.73001); the present one gives more detailed information about different constitutive equations, solutions, etc. than on the physical background or the basics of continuum mechanics. It is not recommended as an introductory textbook for students, but rather as a source of detailed information about that part of Rational Continuum Mechanics, where the most work and development has been achieved.
It is impossible to adequately review the contents of this work here. Instead, we just give a very incomplete list of keywords: deformation tensors, stress analysis, material frame-indifference, material symmetry, boundary value problems, ellipticity, energy principles, monotonicity and convexity, materials of Signorini, Murnaghan, John, Blatz and Ko solutions, second order effects, constraints, small deformations superimposed upon large ones (stability), thermoelasticity. Different appendices contain a representation of the mathematical tools being used, such as (tensor) algebra and analysis, and differential geometry.
Unfortunately, the edition could be better. The book is a copy of a typewriter’s script, who’s variety of different symbols is extremely poor. This fact reduces the clearness of the formulas. Moreover, no list of notations can be found, neither figures nor graphics help for more understanding.
Reviewer: A.Bertram

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
74A40 Random materials and composite materials