11R19. Cosserat Theories: Shells, Rods and Points. Solid Mechanics and its Applications, Vol 79. - MB Rubin (Fac of Mech Eng, Technion-Israel Inst of Tech, Haifa, Israel). Kluwer Acad Publ, Dordrecht, Netherlands. 2000. 480 pp. ISBN 0-7923-6489-9. $205.00.
Reviewed by AH Cardon (Dept of Mech of Mat and Construct, Free Univ Brussels, Pleinlaan 2, Brussels, B1050, Belgium).
This book by Rubin on Cosserat theories is an excellent textbook on the subject with more specific applications to shells, rods, and even points. The book is published as part of the famous series on Solid Mechanics and its Applications, edited by GML Gladwell. This work can be of great help for research engineers and scientists who have to design one- or two-dimensional structural components and who want to understand the basic aspects of those elements out of the one- and two-dimensional analysis without the return to a complete three-dimensional theory.
This book is not of easy access, but the systematic presentation makes it easy to follow and very interesting as further reference work on aspects that were not read in detail during a first lecture.
A short general introduction to the Cosserat model includes an overview not only of the early developments (1893, 1909, 1961, 1972), but also of the more recent applications to many physical problems from electromagnetic effects, over turbulence, microcrack growth, composite materials, plasticity, special behavior of granular media, size effects in rocks to micromechanics of inclusions, and failure of welds. This is followed by an outline of the book showing very clearly the structure of the approach from the basis to the numerical solutions.
In order to have a good basis, Chapter 2 gives an introduction to the basic tensor operations in curvilinear coordinates completed by an Appendix (A) on tensor operations and a short Appendix (B) on specific coordinate systems, polar and spherical.
Chapter 3 reviews the basic equations for the motion of a three-dimensional continuum starting with the balance laws. Further on, anisotropic and isotropic nonlinear elastic materials are discussed followed by a small strain theory and the problem of small deformations superimposed on a large deformation. After some examples, vibrations are analyzed, and in fine a short description is given of the dissipation inequality and the material damping.
The following three chapters (4, 5, and 6) have a similar structure related to the Cosserat theory of Shells (Ch 4), Rods (Ch 5) and Points (Ch 6). In those chapters after description of the Cosserat model, the balance laws are derived from the 3-dimensional theory and by the direct approach. The anistropic nonlinear behavior is followed by a small strain theory, some applications for bending and torsion, vibrations, membranes (Ch 4), strings (Ch 5), the linear theory, the dissipation inequality, and the material damping.
Chapter 7 considers the Cosserat approach to numerical solution procedures in continuum mechanics in general, followed by numerical solution for the Cosserat shell, and the numerical solutions of string, rods, and two- and three-dimensional problems using the theory of the Cosserat point.
After the two appendices, the author introduces some 248 exercises on all the chapters in order for the reader to arrive at a good understanding of the content of the book.
The book is completed by an extensive reference list of some 150 titles and a very good index. The presentation of the book is excellent, and the few figures are of good quality. The stated aims of the author are succeeded by the content and the structure of the book. Cosserat Theories: Shells, Rods and Points has to be present in the libraries of all civil and mechanical engineering departments as well as in all departments of theoretical and applied solid mechanics. Researchers working on beams, rods, plates, shells, and nonlinear structural mechanics in general will find important support in this reference book.