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Mechanics of continuous media
105
Journal of Non-Newtonian Fluid Mechanics, 3 (1977/1978) 105-106 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
Book Review __.__---..--Mechanics of Continuous 576 pages, $6.90.
~__ Media, by S.C. Hunter,
Ellis Henwood,
Chicester,
I must confess to a bias towards the approach to teaching continuum mechanics that Professor Hunter has adopted in this book. One of the principal aims of the author is to show how the many topics in continuum mechanics, often taught in separate courses, arise from the same basic principles. The level of the text is that of the undergraduate applied mathematician though I am sure that students of other disciplines interested in continuum mechanics will find it useful. The first eight chapters, about one third of the book, is devoted to formulating the equations of motion, conservation of mass and the description of material behaviour by constitutive equations. After a brief introductory chapter we are introduced to the notion of a continuum and its mathematical description. The distinction between the material (Lagrangian) and the spatial (Eulerian) description is clearly made and finally illustrated by means of a well-chosen example. The forces acting on the material of a continuum are described in Chapter 3, leading to the concept of stress and the stress equations of motion. The author avoids the pitfall of general tensor theory and devotes Chapter 4 to suffix notation, which surprisingly many students find difficult, Cartesian tensors and the important description of stress as a second-order tensor, and relevant results in matrix algebra including a proof of the polar decomposition theorem for real 3 X 3 matrices. This last result is used in the following chapter to derive, from geometrical aspects of the deformation, the strain, rate-of-strain, and vorticity tensors. Chapter 6 is devoted to the inv~ian~e principles which valid ~onstitutive equations must satisfy and includes a long discussion of the principle of material indifference, once again illustrated by well-chosen examples. We are then led to the derivation of the constitutive equations of ideal and Reiner-Rivlin fluids in Chapter 7, and elastic and thermo-elastic materials in Chapter 8. I believe that students of all branches of continuum mechanics should be familiar with the ideas presented in these chapters. The remaining eight chapters cover the solution, and the techniques used in the solution, of problems of flow and deformation of specific materials. Of these, three are devoted to non-classical theories: shear flow solutions are found for Reiner-Rivlin fluids in Chapter 9; and the theories of linear viscoelasticity and plasticity are discussed in Chapters 15 and 16. Iiowever, students should be aware that many of the techniques described under classi-
106
cal theories are relevant to solving problems for Almost all the chapters contain problems for self and to which worked solutions are given at sor Hunter has produced a very good text book mend to students and teachers alike.
non-classical materials. the reader to attempt himthe end of the book. Profeswhich I am happy to recom-
R.S. JONES
Journal of Non-Newtonian Fluid Mechanics, 3 (1977/1978) 105-106 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
Book Review __.__---..--Mechanics of Continuous 576 pages, $6.90.
~__ Media, by S.C. Hunter,
Ellis Henwood,
Chicester,
I must confess to a bias towards the approach to teaching continuum mechanics that Professor Hunter has adopted in this book. One of the principal aims of the author is to show how the many topics in continuum mechanics, often taught in separate courses, arise from the same basic principles. The level of the text is that of the undergraduate applied mathematician though I am sure that students of other disciplines interested in continuum mechanics will find it useful. The first eight chapters, about one third of the book, is devoted to formulating the equations of motion, conservation of mass and the description of material behaviour by constitutive equations. After a brief introductory chapter we are introduced to the notion of a continuum and its mathematical description. The distinction between the material (Lagrangian) and the spatial (Eulerian) description is clearly made and finally illustrated by means of a well-chosen example. The forces acting on the material of a continuum are described in Chapter 3, leading to the concept of stress and the stress equations of motion. The author avoids the pitfall of general tensor theory and devotes Chapter 4 to suffix notation, which surprisingly many students find difficult, Cartesian tensors and the important description of stress as a second-order tensor, and relevant results in matrix algebra including a proof of the polar decomposition theorem for real 3 X 3 matrices. This last result is used in the following chapter to derive, from geometrical aspects of the deformation, the strain, rate-of-strain, and vorticity tensors. Chapter 6 is devoted to the inv~ian~e principles which valid ~onstitutive equations must satisfy and includes a long discussion of the principle of material indifference, once again illustrated by well-chosen examples. We are then led to the derivation of the constitutive equations of ideal and Reiner-Rivlin fluids in Chapter 7, and elastic and thermo-elastic materials in Chapter 8. I believe that students of all branches of continuum mechanics should be familiar with the ideas presented in these chapters. The remaining eight chapters cover the solution, and the techniques used in the solution, of problems of flow and deformation of specific materials. Of these, three are devoted to non-classical theories: shear flow solutions are found for Reiner-Rivlin fluids in Chapter 9; and the theories of linear viscoelasticity and plasticity are discussed in Chapters 15 and 16. Iiowever, students should be aware that many of the techniques described under classi-
106
cal theories are relevant to solving problems for Almost all the chapters contain problems for self and to which worked solutions are given at sor Hunter has produced a very good text book mend to students and teachers alike.
non-classical materials. the reader to attempt himthe end of the book. Profeswhich I am happy to recom-
R.S. JONES