Elastic Media with Microstructure II

Inhaltsverzeichnis

• 1. Introduction.
• 2. Medium of Simple Structure.
• 2.1 Quasicontinuum.
• 2.2 Equations of Motion.
• 2.3 Elastic Energy Operator.
• 2.4 Symmetric Stress Tensor and Energy Density.
• 2.5 Homogeneous Media.
• 2.6 Approximate Models.
• 2.7 Cubic Lattice.
• 2.8 Isotropic Homogeneous Medium.
• 2.9 Debye Quasicontinuum.
• 2.10 Boundary-Value Problems and Surface Waves.
• 2.11 Notes.
• 3. Medium of Complex Structure.
• 3.1 Equations of Motion.
• 3.2 Energy Operator.
• 3.3 Approximate Models and Comparison with Couple-Stress Theories.
• 3.4 Exclusion of Internal Degrees of Freedom in the Acoustic Region.
• 3.5 Cosserat Model.
• 3.6 Notes.
• 4. Local Defects.
• 4.1 General Scheme.
• 4.2 Impurity Atom in a Lattice.
• 4.3 Point Defects in a Quasicontinuum.
• 4.4 System of Point Defects.
• 4.5 Local Inhomogeneity in an Elastic Medium.
• 4.6 Homogeneous Elastic Medium.
• 4.7 The Interface of Two Media.
• 4.8 Integral Equations for an Inhomogeneous Medium.
• 4.9 Ellipsoidal Inhomogeneity.
• 4.10 Ellipsoidal Crack and Needle.
• 4.11 Crack in a Homogeneous Medium.
• 4.12 Elliptic Crack.
• 4.13 Interaction Between Ellipsoidal Inhomogeneities.
• 4.14 Notes.
• 5. Internal Stress and Point Defects.
• 5.1 Internal Stress in the Nonlocal Theory.
• 5.2 Geometry of a Medium with Sources of Internal Stress.
• 5.3 Green’s Tensors for Internal Stress.
• 5.4 Isolated Point Defect.
• 5.5 System of Point Defects.
• 5.6 Notes.
• 6. Dislocations.
• 6.1 Elements of the Continuum Theory of Dislocations.
• 6.2 Some Three-Dimensional Problems.
• 6.3 Two-Dimensional Problems.
• 6.4 Screw Dislocations.
• 6.5 Influence of Change of the Force Constants in Cores of Screw Dislocations.
• 6.6 Edge Dislocations.
• 6.7 Notes.
• 7. Elastic Medium with Random Fields of Inhomogeneities.
• 7.1 Background.
• 7.2 Formulation of the Problem.
• 7.3 The Effective Field.
• 7.4 Several Mean Values of Homogeneous Random Fields.
• 7.5 General Scheme for Constructing First Statistical Moments of the Solution.
• 7.6 Random Field of Ellipsoidal Inhomogeneities.
• 7.7 Regular Structures.
• 7.8 Fields of Elliptic Cracks.
• 7.9 Two-Dimensional Systems of Rectilinear Cuts.
• 7.10 Random Field of Point Defects.
• 7.11 Correlation Functions in the Approximation by Point Defects.
• 7.12 Conclusions.
• 7.13 Notes.
• Appendices.
• A 1. Fourth-Order Tensors of Special Structure.
• A 2. Green’s Operators of Elasticity.
• A 4. Calculation of Certain Conditional Means.
• References.