Heterogeneous Media

Most materials used in contemporary life and industry are heterogeneous (composites) and multicomponent, possessing a rich and complex internal structure. This internal structure, or microstructure, plays a key role in understanding and controlling the continuum behavior, or macroscopic, of a wide variety of materials. The modeling process is a critical tool for scientists and engineers studying the analysis and experimentation for the micromechanics and behavior of these materials. "Heterogeneous Media" is a critical, in-depth edited survey of the major topics surrounding the modeling and analysis of problems in micromechanics of multicomponent systems, including conceptual and practical aspects. The goal of this extensive and comprehensive survey is to provide both specialists and nonspecialists with an authoritative and interdisciplinary perspective of current ideas and methods used for modeling heterogeneous materials behavior and their applications. Topics and Features: * all chapters use interdisciplinary modeling perspective for investigating heterogeneous media*Five chapters provide self-contained discussions, with background provided*Focuses only upon most important techniques and models, fully exploring micro-macro interconnections*extensive introductory survey chapter on micromechanics of heterogeneous media*microstructure characterization via statistical correlation functions*micro-scale deformation of pore space*wave fields and effective dynamical properties*modeling of the complex production technologies for composite materials The book is ideal for a general scientific and engineering audience needing an in-depth view and guide to current ideas, methods and

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.