Heterogeneous Media

Elementary Micromechanics of Heterogeneous Media.- 1.1 Introduction.- 1.2 The homogenization problem.- 1.3 Some basic results.- 1.4 The single inclusion problem.- 1.5 One-particle approximations.- 1.6 Elastic properties of polycrystals.- 1.7 References.- Diffusion-Absorption and Flow Processes in Disordered Porous Media.- 2.1 Introduction.- 2.2 Microstructure functions.- 2.3 Steady-state trapping problem.- 2.4 Time-dependent trapping problem.- 2.5 Steady-state fluid permeability problem.- 2.6 Time-dependent flow problem.- 2.7 Variational principles for trapping problem.- 2.8 Variational principles for flow problem.- 2.9 Bounds on trapping constant.- 2.10 Bounds on fluid permeability.- 2.11 Cross-property relations.- 2.12 References.- Self-Consistent Methods in the Problem of Wave Propagation through Heterogeneous Media.- 3.1 Introduction.- 3.2 The main hypotheses of the methods.- 3.3 Integral equation of the diffraction problem.- 3.4 General scheme of the effective field method.- 3.5 General scheme of versions I and II of the EMM for matrix composite materials.- 3.6 The solutions of the one-particle problems of version I of the EMM and of the EFM.- 3.7 Asymptotics of the solutions of the dispersion equations.- 3.8 Versions II and III of the EMM in the case of spherical inclusions.- 3.9 Version I of the EMM and the EFM in the case of isotropic random sets of inclusions.- 3.10 Versions I, II, and III of the EMM for matrix composite materials.- 3.11 An approximate solution of the one-particle problem.- 3.12 The EFM for composites with regular lattices of spherical inclusions.- 3.13 Versions I and IV for polycrystals and granular materials.- 3.14 Discussion.- 3.15 Conclusions.- 3.16 References.- Deformable Porous Media and Composites Manufacturing.- 4.1 Introduction.- 4.2 Ensemble average approach.- 4.3 Effective media approach.- 4.4 Deformable and saturated porous media models.- 4.5 Boundary conditions.- 4.6 One-dimensional infiltration.- 4.7 Simulations.- 4.8 Three-dimensional unsaturated isothermal model.- 4.9 Open problems.- 4.10 References.- Micromechanics of Poroelastic Rocks.- 5.1 Introduction.- 5.2 Hydrostatic poroelasticity.- 5.3 Undrained compression.- 5.4 Constitutive equations of linearized poroelasticity.- 5.5 Equations of stress equilibrium and fluid flow.- 5.6 Dependence of poroelastic parameters on pore structure.- 5.7 Conclusions and future directions.- 5.8 References.