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Understanding viscoelasticity. Basics of rheology. (English) Zbl 1036.74001
Berlin: Springer (ISBN 3-540-43395-3/hbk). xiii, 145 p. (2002).
This book is a good introduction to the theory of viscoelasticity. The author presents the fundamentals of continuum mechanics together with mathematical background in a unified description. The book consists of eight chapters: 1. Tensor notation; 2. Rheological properties; 3. Kinematics and equations of balance; 4. Constitutive equations; 5. Inelastic models and linear viscoelasticity; 6. Steady viscometric flows; 7. Polymer solutions; 8. Suspensions. The book also contains a bibliography and an index.
In the first chapter the author presents the basic rules of tensor calculus and mathematical concepts needed in the sequel. The second chapter is a review of non-Newtonian behaviour in flows. Chapter 3 is concerned with kinematics and balance laws (conservation of mass, balance of momentum, balance of energy). Chapter 4 gives a treatment of constitutive equations (classical constitutive equations, axioms of constitutive theory, symmetry restrictions, simple materials). In Chapter 5 some practical engineering inelastic and elastic models are presented. Chapter 6 is devoted to viscometric flows in which both the kinematics and stress are determined by the flow, irrespective of the constitutive equations. In Chapter 7 the constitutive modelling of dilute polymer solutions is discussed. Finally, Chapter 8 is concerned with a study of suspensions.
The book gives a detailed and clear treatment of the subject. Each chapter contains interesting problems. On balance, this is a useful work.

74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
76A10 Viscoelastic fluids
74A20 Theory of constitutive functions in solid mechanics
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
76T20 Suspensions