5R2. Continuum Mechanics. - I-Shih Liu (Inst de Matematica, Univ Federal do Rio de Janeiro, CP 68530, Rio de Janeiro, 21945-970, Brazil). Springer-Verlag, Berlin. 2002. 297 pp. ISBN 3-540-43019-9. $54.95.
Reviewed by E DeSantiago (Dept of Civil and Architec Eng, Illinois Inst of Tech, 3201 S Dearborn St, Rm 213, Chicago IL 60616-3793).
This book is intended primarily as a textbook for graduate students and advanced undergraduate students in theoretical physics, applied mathematics, and engineering sciences. The text can also serve as a reference book for students and researchers in the fields of applied and structural mechanics. The text begins with a general discussion of kinematics in Chapter 1 and the basic balance laws in Chapter 2. Chapter 2 also includes formulations for the balance laws in which jump conditions exist due to singularities in the continuum fields. Chapter 3 contains a very general and thorough discussion of constitutive theories in which the principles of material objectivity and material symmetry are presented. Chapter 4 continues the discussion on constitutive formulations and particular emphasis is placed on deriving a reduced set of variables for these formulations using basic principles.
Chapter 5 introduces entropy principles and the resulting Clausius-Duhem inequality. Discussions on the restrictions placed on constitutive formulations by entropy principles and the role entropy production plays in the stability of equilibrium solutions is also included in this chapter. Chapter 6 emphasizes the application of previously derived principles to isotropic elastic solids. In this chapter the problems of biaxial stretching, pure shear of a square block, and the finite deformation of spherical shells are solved and presented. Chapter 7 introduces the concept of utilizing Lagrange multipliers for exploiting the entropy principle for a viscous heat-conducting fluid. Chapter 8 includes a brief lecture on the relatively new approach for formulating the basic equations termed rational extended thermodynamics. In this approach, the momentum flux and the energy flux are also taken as basic field quantities in addition to the densities of mass, momentum, and energy leading to simpler constitutive relations but at the cost of more complex basic fields. Finally, the text concludes with an appendix in which a short introduction to linear algebra and tensor calculus is included.
The objective of the author is to present the theory of continuum mechanics from a rational framework that emphasizes basic principles. The strength of the book lies in the presentation of a very general and rational the framework for constitutive formulations and the role thermodynamics plays in these formulations. The discussions on kinematics and force (stress) concepts, on the other hand, are not as thorough as those found in other text on the same subject matter. With the exception of Chapter 6, very few applications to physical problems are presented. Instead the author includes exercises and figures that emphasize the derivation and application of basic principles and theories to further the understanding of the material. It is clear from the presentation of the material that more emphasis was placed on constitutive formulations and thermodynamics than was the case for mechanical concepts.
In summary, Continuum Mechanics is recommended more as a reference book for students and researchers in applied mechanics and structural mechanics who are interested in a more thorough treatment of constitutive formulations and the role thermodynamics plays in these formulations. The text is also recommended as a textbook for studentsin the fields of theoretical physics and applied mathematics for which a more rational framework of continuum mechanics is required.