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A first course in rational continuum mechanics. Vol. 1. 2nd ed. (English) Zbl 0866.73001

Pure and Applied Mathematics, 71. Boston, MA: Academic Press. xviii, 391 p. (1991).
Rare are those authors who, when being offered the possibility of publishing a second edition of their work, present a thorough revision with numerous additions. We must be grateful to the author who has undertaken such a courageous tremendous task in presenting us with this second edition of his now classic first edition [Academic Press, London (1977; Zbl 0357.73011)]. Indeed, hardly a page from the first edition remains unamended and the total work has grown by almost one quarter, thus paving the way for the much delayed second and third volumes. Let us recall that this treatise, originally projected in three volumes, has a strange prehistory as shorter versions of the first volume have appeared in French (1973) and Russian (1975) but, to our knowledge, enjoyed only limited circulation as they hardly met the style of teaching continuum mechanics in France or Russia in those days. The first English edition (1977) was much better received and reamains as a paragon of teaching continuum mechanics in Lagrange’s style, i.e., analytically above all and without the support of any figures (this second edition remains faithful to this Lagrangean spirit, incorporating no figures, a practice certainly not shared by all of us). Of special interest are the corrections, improvements and additions brought to this new edition. Most of these aim at clarifying, compacting or extending what was known at the time of the first edition. Thus, although many parts of the text have been rephrased, we particularly note the revision of sections dealing with rigid frames in general (I.6) and changes of frames (I.9), placements and so-called “universes of shapes” (II.1), the notions of force and torque in continuum mechanics (III.1; following recent work by W. Noll and E. G. Virga [Arch. Ration. Mech. Anal. 102, No. 1, 1-21 (1988; Zbl 0668.73005)], simple bodies (IV.8) and universal motions (which are independent of the material; IV.10), the recasting of sections dealing with universal homogeneous motions (IV.9-10) and monotonous motions (IV.21), and the welcome addition of sections on universal transplacements (“motions” for the layman) of isotropic incompressible bodies (IV.16) and flows of homogeneous incompressible fluids (these are more solution-oriented than the rest of the volume which strictly adheres to generalities), and a brief addendum on internal energy (I.15).
As remarked at the beginning of this review, the style entertained is the one proper to the school created by Truesdell. It is marked by mathematical rigor combined with an obsessive care for language and an excessive use of neologisms which nowadays are not cultivated in many places and which, like Bourbaki in pure mathematics, have often been responsible for a rejection of otherwise deep and useful concepts by many practioners not formed in the arcanum of the same formalism. Nonetheless, this second revised version is most welcome and we look forward to the expected publication of Volumes II and III, respectively devoted to fluids and elastic bodies.

MSC:

74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
76A02 Foundations of fluid mechanics
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