11R26. Mechanics of Deformable Solids: Linear and Nonlinear, Analytical and Computational Aspects. - I Doghri (CESAME, Universite catholique de Louvain, Euler Bldg, 4 Ave G Lemaitre, Louvain-la-Neuve, B-1348, Belgium). Springer-Verlag, Berlin. 2000. 579 pp. ISBN 3-540-66960-4. $84.95.
Reviewed by DS Chandrasekharaiah (Dept of Math, Bangalore Univ, Central Col Campus, Bangalore, Karnataka, 560 001, India).
This is a comprehensive introductory textbook that deals with the nondynamical theory of deformable solids and structures. Emphasis is put on the linear and nonlinear, as well as the analytical and computational aspects of the theory. The book is meant for students and researchers in mechanical and civil engineering, material science, and related fields.
The book contains as many as 20 chapters. Chapters 1 to 13 deal with the linear theory; Chapters 14 to 19 deal with the nonlinear theory; and the last chapter deals with microstructures. The classical linear theory of isotropic elastic materials is covered in Chapters 1 to 8; it includes the following: 1) a recapitulation of the governing equations of the theory, 2) variational formulation, and work and energy theorems, 3) theory of bending and torsion of beams, 4) theory of bending of thin plates, and 5) plane strain and plane stress problems. Although all these items can be found in most books on elasticity, the novelty in this book is that they are presented in an easily digestible, piece-meal form. However there is a deficiency: The complex variable method, which is an integral part of two-dimensional elasticity theory, is conspicuous by its absence.
The topics of thermoelasticity, elastic stability, theory of thin shells, elastoplasticity, and elastoviscoplasticity are considered in Chapters 9 to 13. Compared to earlier chapters, these chapters are sketchy. The approach to thermoelastic problems in Chapter 9 is ad hoc in nature, and the stray problems solved therein give little insight into the subject of thermomechanics. Chapter 10 is successful in its limited aim of giving a glimpse of the notion of elastic stability. Citing of references for further reading enhances the usefulness of Chapters 11 to 13.
The nonlinear continuum theory in general and the nonlinear elasticity theory in particular are presented in Chapters 14 and 15, respectively. The theories have been formulated in a systematic, logical, and appealing way. These chapters provide a good foundation material for further studies on nonlinear mechanics.
Chapter 16 and 17 deal with the topics of nonlinear elastoplasticity and cyclic plasticity, respectively. Chapters 18 and 19 are concerned with damage mechanics and strain localization. In these chapters, various constitutive models have been formulated. The algorithms presented and the references cited for further reading are aimed at researchers in the respective areas.
The final chapter is concerned with micromechanics. Here, the coverage is inadequate, even for the beginner. The references cited for further reading do not include well-known works on this important modern area.
On the whole, this book makes pleasant reading. Chapters 9 (Thermoelasticity) and 20 (Micromechanics of materials) are weak, but the other chapters are well balanced and lucidly presented. Appropriate care has been taken in the use of direct, suffix, and matrix notations. The bibliography is extensive. The index is satisfactory. The layout of the book and the figures are good.
Mechanics of Deformable Solids, by I Doghri, is a welcome addition to the textbook literature on Solid Mechanics. This reviewer recommends the book to anyone who is interested in having a sound, basic knowledge of linear and nonlinear theories of elasticity and allied areas.