Erratum: Nonlinear Continuum Mechanics of Solids: Fundamental Mathematical and Physical Concepts

Abstract

11R2. Nonlinear Continuum Mechanics of Solids: Fundamental Mathematical and Physical Concepts. - Y Basar (Inst fur Statik und Dynamik, Ruhr-Univ Bochum, Universitatsstr 150, Bochum, 44780, Germany) and D Weichert (Inst fur Allgemeine Mech, RWTH Aachen, Templergraben 62, Aachen, 52056, Germany). Springer-Verlag, Berlin. 2000. 193 pp. ISBN 3-540-66601-X. $59.95.Reviewed by J Petrolito (Sch of Sci and Eng, La Trobe Univ, PO Box 199, Bendigo, Vic 3350, Australia).This is a graduate-level textbook on the fundamental concepts of nonlinear solid mechanics. The authors’ stated goal is to provide students with sufficient background to carry out research in this area. As such, the book emphasizes the theoretical aspects of the subject rather than dealing with specific applications. However, given that this is a textbook, it is surprising that there are not many exercises to help students reinforce their learning.The book, divided into six chapters and an appendix, makes extensive use of tensor analysis, and the first chapter discusses the basic aspects of this theory. This chapter is complemented by the appendix on index notation and general coordinate systems. The combination serves as a concise introduction to tensor analysis in its own right. The second chapter is concerned with the concepts of deformation and strain. There is considerable discussion on the distinction between material and spatial coordinates and the conversions between the two systems. Various nonlinear strain measures are defined, and these are shown to be particular cases of a unified definition of strain. In total, the first two chapters take up around half the book. Chapter 3 discusses the concept of stress and shows how different stress measures are associated with appropriate energy-conjugate strain measures. This is followed by a very short chapter on time derivatives that could have been incorporated into Chapter 2. The next chapter discusses the various balance laws in mechanics and includes a brief discussion on the principle of virtual work. The final chapter details the requirements of constitutive relationships, with particular emphasis on elastic materials.It is interesting to compare this book with another recent book that broadly covers the same area 1. Both books emphasize theory over practical applications, with 1 taking a more abstract approach to the subject. The current book, being around twice the length, devotes considerably more attention to tensor analysis and its use in solid mechanics. But ultimately, both books stop too soon. While they clearly develop the basic concepts, neither book provides any significant insight on how to apply the theory in practice. Even a short chapter on some typical applications would have enhanced both books.In summary, the current book, Nonlinear Continuum Mechanics of Solids: Fundamental Mathematical and Physical Concepts, provides a useful introduction to the theoretical aspects of nonlinear solid mechanics at the graduate level. It will appeal to students who want to quickly gain an understanding of the basic principles. Students who need guidance on particular problems in the area will need to look to other books for this.