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.

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.

Reviewer: Dorin Ieşan (Iaşi)

##### MSC:

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 |