Understanding Viscoelasticity: Basics of Rheology , Nhan Phan-Thien Springer-Verlag, New York, 2002. $34.95 (145 pp.). ISBN 3-540-43395-3
In Understanding Viscoelasticity: Basics of Rheology, Nhan Phan-Thien, who has produced several substantial contributions in rheology over the past three decades, provides a concise account of the behavior of real materials. Most materials, such as the now ubiquitous polymeric composites, display a behavior somewhere between that of ideal (inviscid) fluids and ideal rigid solids. That is to say, they are viscoelastic.
Suitable as a text for a first-year graduate course in viscoelastic materials, the book provides students with some necessary tools to read and better understand technical articles in the field.
Phan-Thien sensibly introduces the reader to a mesoscopic approach to modeling. Although one would prefer to use molecular theories for macromolecular dynamics, their quantitative predictions for a variety of material functions are not yet compatible with reliable predictions derived from theories based in continuum mechanics. Until such compatibility evolves, hybrid continuum—particle theories should help to improve physical understanding of mesoscopic phenomena and to suggest directions for the more fundamental molecular-theory approach.
Among the book’s many positive attributes are the clear introductory remarks that begin each chapter. Concepts leading to material functions are well introduced and defined. Nice historical tidbits, sprinkled throughout, convey valuable information on scientists of note and the remarkable scientific advances for which they are famous. Homework problems with ample pedagogical and mnemonic value appear at the end of each chapter. Given its extensive mathematical content, the book is remarkably free of typographical errors.
The conciseness of Phan-Thien’s text is reminiscent of other such important works as William Schowalter’s Mechanics of Non-Newtonian Fluids (Pergamon Press, 1978) and Arthur Lodge’s An Introduction to Elastomer Molecular Network Theory (Bannatek Press, 1999), both of which deal tersely and at a rather advanced level with viscoelastic materials.
The book’s conciseness can sometimes be a liability. For example, group theory and functionals are mentioned in only a few short paragraphs. Also, the book limits its summary of tensor analysis to Cartesian tensors, whereas Rheology of Polymeric Systems: Principles and Applications, by Pierre Carreau, Daniel De Kee, and Raj Chhabra (Hanser, 1997), provides a more comprehensive account of generalized curvilinear coordinate systems and higher-order tensors. A longer and more complete account of such topics of interest as stress, strain, and constitutive equations can be found in Cemal Eringen’s Mechanics of Continua (Krieger, 1980). Finally, a list of modern nomenclature is absent and would have been helpful.
The pedagogically astute homework problems are designed to deepen a student’s understanding. However, in some cases, such understanding would require a mathematical maturity that students may lack, given the current content of most undergraduate engineering curricula.
Despite the few limitations imposed by the book’s brevity, Understanding Viscoelasticity is a joy to read and will be very useful to motivated students.
