1R1. Tensor Analysis and Continuum Mechanics. - YR Talpaert (Dept of Sci and Eng, Algiers Univ, Algeria). Kluwer Acad Publ, Dordrecht, Netherlands. 2002. 591 pp. ISBN 1-4020-1055-9. $161.00.
Reviewed by JG Simmonds (Dept of Civil Eng, Univ of Virginia, Thornton Hall, Charlottesville VA 22903).
This is a carefully written treatise that begins by (over?) developing the tensor machinery necessary to state and manipulate various global and local forms of the general equations of continuum mechanics (conservation of mass, translational and rotational momentum, first and second laws of thermodynamics, excluding chemical and electromagnetic effects). Each of the book’s six chapters ends with a good number of worked-out exercises. Although considerable attention is given to the kinematics and kinetics of deforming continua, the important topic jumps and shocks are not treated and the only specific constitutive relations considered are those of linear elasticity, mostly for isotropic bodies.
However, no matter how well done, one must ask in such a well-plowed field as continuum mechanics if a new book supercedes in any way—novelty of presentation, new insights into well-established principles and equations, range of phenomena, or variety of constitutive relations—some of the older, standard treatments, such as those of Truesdell and Toupin (1960), Truesdell and Noll (1965), Chadwick (1976), Spenser (1980), Gurtin (1981), or Truesdell (1984, 1991). Unfortunately, in my opinion, the answer is “No.” (Incidentally, none of the books just cited appears in the author’s list of references.)
By no means am I implying that continuum mechanics is a closed field. But it seems to me that today’s focus is on the establishment, analysis, and implications of ever more comprehensive constitutive relations, an area that the author of the book under review barely touches.
In summary, Tensor Analysis and Continuum Mechanics is a sound, well-written book, suitable for a first-year graduate course, but researchers in the various branches of continuum mechanics will find little that is new.
