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Nonlinear continuum mechanics of solids. Fundamental mathematical and physical concepts. (English) Zbl 0946.74001

Berlin: Springer. x, 193 p. (2000).
This book is designed for graduate students of engineering and material sciences, applied mathematicians and research engineers. The authors present the fundamentals of continuum mechanics of solids together with the necessary mathematical background in a unified description.
The book consists of six chapters: 1. Mathematical fundamentals; 2. Deformation; 3. Stresses; 4. Time derivative; 5. Balance laws; 6. Constitutive modelling. The book also contains an appendix, a bibliography and an index.
In the first chapter the authors present the basic rules of tensor calculus in absolute notation and the mathematical concepts needed in the sequel. The second chapter treats the geometry of deformations, strain measures, rate-of-deformation tensors and spin tensors. Stress tensors are described in chapter 3. In chapter 4, the authors introduce the notion of material time derivatives, and study material time derivatives of various geometrical variables. Chapter 5 is concerned with balance laws (conservation of mass, balance of momentum, balance of moment of momentum, balance of energy). Finally, chapter 6 presents the theory of constitutive equations (general principles, objective tensors, elastic materials, hyperelastic materials, St.Venant-Kirchhoff material, Hookean materials, linear constitutive equations). Each chapter contains applications illustrating the theory.
In reviewer’s opinion, the book is a useful work.
Reviewer: D.Ieşan (Iaşi)

MSC:

74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74A20 Theory of constitutive functions in solid mechanics
74A05 Kinematics of deformation
74A10 Stress
74B20 Nonlinear elasticity
74B05 Classical linear elasticity
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