Anelastic Relaxation in Crystalline Solids

Abstract

Rheological fluid mechanics is an intellectually interesting and technologically important subject.The reason that this subject has not come into a more central place in fluid mechanics is because of uncertainty about the correct form for the governing equations.Constitutive relations which are general enough to describe the tremendously varied responses open to a Theologically complex fluid are too general to solve many problems.And specific constitutive equations, developed from models, suitable for problem solving, are at best guided guesses which leave open the ultimate question about whether the constitutive relation you give is the right one for the fluid you got.Authors have had to decide between a good treatment of principles, without much problem solving, and a good treatment of fluid models, emphasizing problem solving.In the first category the treatise by Truesdell and Noll (The Nonlinear Field Theories of Mechanics, Springer, 1965) is without peer; in the second category are the books of Lodge (Elastic Liquids, Academic Press, 1964), and Middleman (The-Flow of High Polymers, 1968).The book by Astarita and Marrucci follows the line of thought developed by Truesdell and Noll, but from their own more pragmatic point of view and with some attention in the last two of seven chapters, to methods of approach toward solving important problems in the fluid mechanics of non-Newtonian fluids.The book is simply and clearly written.The arrangement of material is good and the book may be read, cover to cover.The technical arrangements for printing text, equations, and notes is outstanding and, in this, the authors and McGraw-Hill have produced an excellent work.Non-Newtonian Fluid Mechanics cannot, of course, be compared to the Nonlinear Field Theories in breadth, rigor, and depth of scholarship.But the Truesdell and Noll book is full of new concepts, notations, and modes of thought and to say the least, demands more than some ordinary folk can give and more than lessordinary folk will give.Since understanding is always incomplete, it is just a matter of degree, and a more gentle introduction to the theory of nonlinear continuum fluid mechanics developed by Coleman, Ericksen, Noll, Rivlin, Truesdell, and others is most welcome.The Astarita and Marrucci book gives this more gentle introduction.It achieves this greater simplicity in presentation by deleting materials which are not directly related to fluids, by sacrificing completeness and by omitting difficult mathematical demonstrations.