Elastic Media with Microstructure II

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.