The non-linear field theories of mechanics. 2. ed. (English) Zbl 0779.73004

Berlin: Springer-Verlag. x, 591 p. (1992).
When the first edition of this book appeared in 1965, it was just during the heyday of what people called “Rational Mechanics”. And especially this book took over the part to propagate these ideas worldwide. It presented a more or less complete compendium of the knowledge of the material behavior of continuous bodies undergoing finite deformations. At that time this meant just elasticity, hypo-elasticity, and viscosity, apart from the basic concepts of continuum mechanics. Rational theories on finite viscoelasticity and fading memory were still in a premature state at that time, and finite plasticity was (and perhaps still is) far from deserving the label “rational”.
Few books in this century, if any, have influenced continuum mechanics, and especially its part of material theory, more than this volume of the Encyclopedia of Physics of 1965, both as regards teaching and research. This fact is not only due to the completeness, but also to the clearness and correctness of the presentation. Consequently, but unfortunately, it was out of print for decades, and the reprint of 1992 came far too late.
After so much time the subject has undergone an enormous amount of development, not only by addition to the knowledge of the sixties, but also by radical changes and corrections of even the most fundamental approaches. Let us give just one example. Already in 1972 W. Noll stated that the concept of history functionals was too limited and essentially excluded all theories of plasticity. Moreover, this concept was not acceptable as a general one, neither from a philosophical nor from a practical point of view. Accordingly, Noll suggested his “new mathematical theory of simple materials” giving a completely new framework for material theory. Unfortunately, this theory has been widely ignored by the scientific community, that still thinks in terms of the old and inadequate functionals.
For this reason, giving a mere up-date of the 1965 version was not appropriate. The two authors did the best they could do, namely to conserve the book by reissuing it in its original form. Only “typographical errors and minor infelicities of style” have been emended and some incorrect statements have been marked in the new edition. And in this form it will surely enter the history of our subject as a milestone and still serve those working in this field as a precious source of information, that should be available in every scientific library.
Reviewer: A.Bertram (Berlin)


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