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Practical Aspects of Finite Element Modeling of Polymer Processing Vahid Nassehi (John Wiley & Sons, West Sussex, 2002) 273 pages, $135.00 ISBN 0-471-490-42-3 This is a nice, concise book of use to beginners and practitioners wanting to learn how to apply the finite element method to some problems in polymer processing. Virtually all the topics and considerations of the finite element method are mentioned; some of them are described in detail. Solutions are given for several polymer-processing applications. The source code for a finite element program is included, but it only applies to power-law fluids in two dimensions, in steady, creeping motion. However, with the differential equations in the book, the element equations in the book, and the program, the beginner can immediately apply the finite element method to some polymer-processing problems. To extend the program to axisymmetric geometry and to viscoelastic fluids, for example, is not a big stretch because all the differential equations and element equations are given in the book. Thus, the book strikes a good balance between being simple enough to understand and being able to solve real problems. The reader should not expect the program to solve viscoelastic problems or even very many real problems. Chapter 1 gives a quick trip through constitutive equations, using dyadic notation. Chapter 2 describes finite elements and shows how to set up finite element problems including streamwise upwinding and the Petrov–Galerkin method. Chapter 3 includes almost all of the major ideas involving finite elements and polymers, even if they are not implemented in the computer code provided. Chapter 4 writes down the working equations for Cartesian, polar, and axisymmetric problems (all two-dimensional), and for continuous and discrete penalty methods for pressure. The time-dependent scheme presented is a specialized technique, but the important work of Gresho, Lee, and Sani at Lawrence Livermore National Laboratory should have been given more prominence. Chapter 5 gives results of several polymer-processing examples done by the author. They include applying the volume of fluid (VOF) method to a singleblade mixer, applying the Arbitrary Lagrange–Euler method to a twin-blade mixer, Couette flow of rubber analyzed with a generalized Newtonian fluid and VOF or with a Maxwell viscoelastic fluid with a Lagrangian method. These results MRS BULLETIN/AUGUST 2003

show that the generalized Newtonian fluid does not give the proper normal stresses that the viscoelastic fluid shows, and it would have been nice to have seen the Criminale, Ericksen, and Filbey (CEF) results as well. The Phan-Thien/ Tanner viscoelastic model is applied in a timedependent problem for a segment of a screw, and a rubber mixer with slip is modeled. The last two problems are a cone and plate viscometer (for a Maxwell fluid) and a thin-layer extrusion. This book will be of interest to someone wanting to write computer codes, and it is clearly presented for that use. Someone only interested in the gen

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