Microcontinuum Field Theories I. Foundations and Solids
Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. Material bodies are here viewed as collections of large numbers of deformable particles, much as each v...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1999, 1999
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| Edition: | 1st ed. 1999 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Kinematics
- 1.0 Scope
- 1.1 Physical Picture
- 1.2 Motions and Deformations
- 1.3 Rotation
- 1.4 Microstretch and Micropolar Continua
- 1.5 Strain Measures
- 1.6 Relative Motion, Relative Strain Measures
- 1.7 Compatibility Conditions
- 1.8 Material Time-Rate of Tensors
- 1.9 Objective Tensors
- 1.10 Mass, Inertia, Momenta, Kinetic Energy
- 1 Problems
- 2 Stress
- 2.0 Scope
- 2.1 Balance of Energy
- 2.2 Balance Laws
- 2.3 Second Law of Thermodynamics
- 2.4 Dissipation Potential
- 2 Problems
- 3 Constitutive Equations
- 3.0 Scope
- 3.1 Constitutive Equations of Elastic Solids
- 3.2 Constitutive Equations of Fluids
- 3.3 Thermodynamic Restrictions on Solids
- 3.4 Thermodynamic Restrictions on Fluids
- 3.5 Thermodynamic Restrictions on
- Memory-Dependent Solids
- 3.6 Thermodynamic Restrictions on
- Memory-Dependent Fluids
- 3 Problems
- 4 Electromagnetic Interactions
- 4.0 Scope
- 4.1 Balance Laws
- 4.2 Constitutive Equations of E-M Solids
- 5.24 Nonlinear Waves
- 5.25 Fundamental Solutions in Micropolar Elastostatics
- 5.26 Dislocations and Disclinations
- 5.27 Theory of Micropolar Plates
- 5.28 Flexural Waves
- 5.29 Other Contributions
- 5 Problems
- 6 Microstretch Elasticity
- 6.0 Scope
- 6.1 Linear Constitutive Equations
- 6.2 Uniqueness Theorem
- 6.3 Plane Harmonic Microstretch Waves
- 6.4 A Lattice Model for Microstretch Continuum
- 6.5 Fundamental Solutions
- 6.6 Microstretch Surface Waves
- 6.7 Other Solutions
- 6 Problems
- 7 Micromorphic Elasticity
- 7.0 Scope
- 7.1 Linear Constitutive Equations
- 7.2 Passage to Microstretch and Micropolar Theories
- 7.3 Restrictions on Material Moduli
- 7.4 Plane Harmonic Waves
- 7.5 Other Contributions
- 7 Problems
- 8 Electromagnetic Interactions
- 8.0 Scope
- 8.1 Linear Constitutive Equations
- 8.2 Material Stability
- 8.3 Balance Laws
- 8.4 Field Equations
- 8.5 Piezoelectric Waves
- 8 Problems
- References
- 4.3 Constitutive Equations of E-M Fluids
- 4.4 Memory-Dependent E-M Solids
- 4.5 Memory-Dependent E-M Fluids
- 4 Problems
- 5 Theory of Micropolar Elasticity
- 5.0 Scope
- 5.1 Linear Constitutive Equations
- 5.2 Material Symmetry and Stability
- 5.3 Isotropic Solids
- 5.4 Formulation of Problems in Micropolar Elasticity
- 5.5 Mixed Boundary-Initial Value Problems in Linear Theory
- 5.6 Curvilinear Coordinates
- 5.7 Uniqueness Theorem
- 5.8 Reciprocal Theorem
- 5.9 Variational Principles
- 5.10 Conservation Laws
- 5.11 Plane Harmonic Waves
- 5.12 Material Moduli
- 5.13 Experimental Attempts
- 5.14 Displacement Potentials
- 5.15 Micropolar Waves in Half-Space
- 5.16 Micropolar Surface Waves
- 5.17 Micropolar Waves in Plates
- 5.18 Fundamental Solutions
- 5.19 Problems of Sphere and Spherical Cavity
- 5.20 Axisymmetric Problems
- 5.21Penny-Shaped Crack
- 5.22 Stress Distribution Around an Elliptic Hole
- 5.23 Stress Concentration Around a Circular Hole