Heterogeneous Media

This new book contains an edited collection of extensive chapters providing authoritative surveys for modeling composite materials and multiphase flow. The goals is to provide comprehensive, interdisciplinary treatment of current ideas, methods and models used in the micromechanics of heterogeneous media. The book will appeal to applied mathematicians, mechanical engineers, and materials scientists interested in problems in micromechanical analysis and behavior of multicomponent systems.

Contenu
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.