Finite elasticity and viscoelasticity : a course in the nonlinear mechanics of solids /
Aleksey D. Drozdov.
Bok Engelsk 1996 · Electronic books.
latin
| Utgitt | Singapore ; River Edge, N.J. : : World Scientific, , c1996.
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| Omfang | 1 online resource (456 p.)
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| Opplysninger | Description based upon print version of record.. - Contents; Preface; FINITE ELASTICITY AND VISCOELASTICITY; Chapter 1 Tensor calculus; 1. Geometry of Motion; 1.1. Description of Motion; 1.2. Tangent Vectors; 1.3. Transformation of Coordinate Frames; 2. Tensor Algebra; 2.1. Definition of a Tensor; 2.2. Operations on Tensors; 2.2.1. Operation on one tensor; 2.2.2. Operations on two tensors; 2.3. The Unit Tensor; 2.4. An Inverse Tensor; 2.5. Eigenvectors and Eigenvalues of a Tensor; 2.6. The Principal Invariants of a Tensor; 2.7. Expansion of a Symmetrical Tensor into the Spherical and Deviatoric Parts; 2.8. Positive Definite Tensors. - 1.1 The Deformation Gradient1.2. Deformation Tensors and Strain Tensors; 1.3. Stretch Tensors; 1.4. Relative Deformation Tensors; 1.5. Generalized Strain Tensors; 1.6. Rigid Motions; 1.7. Volume Deformation; 1.8. Deformation of the Surface Element; 2. Dynamics of Continua; 2.1. Forces; 2.2. Mass Conservation Law; 2.3. Principle of Linear Momentum; 2.4 The Cauchy Stress Tensor; 2.5. Equation of Motion; 2.6. Principle of Angular Momentum; 2.7. Energy Balance Equation; 2.8. The Piola Stress Tensor; 3. Constitutive Equations; 3.1. Axioms of the Constitutive Theory. - 2.6.3. Strain energy densities as symmetrical functions. - 2.9. Orthogonal Tensors2.10. Polar Decomposition; 2.11. Triangular Decomposition; 3. Tensor Analysis; 3.1. The Nabla-Operator; 3.2. Operators Connected with the Nabla-Operator; 3.3. Properties of the Nabla-Operator; 3.4. Christoffel's Symbols; 3.5. Derivatives of the Dual Vectors; 3.6. Derivative of the Elementary Volume; 3.7. Covariant Derivative of a Vector; 3.8. Covariant Derivative of a Tensor; 3.9. The Ricci Theorem; 3.10. The Divergence of a Vector and a Tensor; 3.11. The Second Covariant Derivative; 3.12. The Stokes Formula; 4. Corotational Derivatives; 4.1. Objective Tensors. - 3.2. Principles of Fading MemoryChapter 3 Constitutive equations in finite elasticity; 1. Elastic Behavior of Materials; 2. Constitutive Equations in Finite Elasticity; 2.1. Elasticity and Hyperelasticity; 2.2. The First Law of Thermodynamics; 2.3. Finger's Formula; 2.4. Constitutive Restrictions; 2.5. Non-convexity and Polyconvexity of Strain Energy Densities; 2.6. Examples of Strain Energy Densities; 2.6.1. Strain energy densities in the form of truncated Taylor series; 2.6.2. Strain energy densities in the form of truncated series in powers of the principal invariants. - 4.2. Velocity and Its Gradient4.3. The Zorawski Formula; 4.4- The Jaumann Derivative; 4.5. The Oldroyd Derivatives; 4.6. The Rivlin-Ericksen Tensors; 5. Tensor Functions; 5.1. The Rivlin-Ericksen Theorem; 5.2. Derivatives of a Scalar Function with Respect to a Tensor Variable; 5.2.1. Derivatives of the principal invariants; 5.2.2. Finger's formula; 5.2.3. Derivatives with respect to the inverse tensor; 5.2.4. The second derivatives of a scalar function with respect to a tensor variable; 5.3. Convex Functions; Chapter 2 Mechanics of continua; 1. Kinematics of Continua. - This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other.A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as w
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| Emner | |
| Sjanger | |
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| ISBN | 1-283-63588-7. - 981-283-061-8
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