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An introduction to continuum mechanics. (English) Zbl 0559.73001
Mathematics in Science and Engineering, Vol. 158. New York - London etc.: Academic Press (Harcourt Brace Jovanovich, Publishers). XI, 265 p. $ 44.00 (1981).
The author is surely one of the most productive researchers in the field of modern continuum mechanics. His contributions to the ’Archive of Rational Mechanics and Analysis’ as well as his article in ”Encyclopedia of Physics, Vol. VI a/2” became well-known because of their axiomatic approach, the use of modern mathematical tools, and their rigorous method of statements and proofs, which has influenced many other authors. It seems remarkable, that Gurtin published this ”Introduction” after fifteen years of teaching experience in this field. The result is a textbook, that shows in each part that continuum mechanics can be founded with almost the same accuracy as geometry and linear algebra.
The book begins with a short review of tensor algebra and analysis. The use of a direct tensor notation attributes to the clarity of the text as well as the formulation of provable facts as propositions and theorems. The physical part introduces general concepts as deformations, motion, mass, force and stress. A general theory of materials is not given, but instead the description of two important classes of materials, namely the Newtonian fluids and the finite and linear elastic bodies. A great number of solutions (motions, flows) is discussed. An appendix on tensor functions as well as a long list of hints for the given exercises in each section is added. References to literature are but few. The reader is referred only to some encyclopedia articles.
All in all, the referent considers this book highly recommendable as an introduction into the rather complicated field of rational mechanics.
Reviewer: A.Bertram

74Axx Generalities, axiomatics, foundations of continuum mechanics of solids
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
76A02 Foundations of fluid mechanics