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Averaging processes in periodic media. Mathematical problems of the mechanics of composite materials. (Osrednenie protsessov v periodicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov). (Russian) Zbl 0607.73009

Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 352 p. R. 4.20 (1984).
Mathematical problems for micro-nonhomogeneous materials have been considered making use of the method of averaging processes in periodic media.
The investigation includes mathematical models for the problems of the theory of elasticity, heat transfer and wave propagation in micro- nonhomogeneous materials as well as diffusion and filtration in porous media. Continuous models for network structures are also presented and the theory of boundary layer for composite materials is developed.
The method of averaging processes used in this monograph enables to determine average and local characteristics of the materials and structures studied and to find asymptotic distributions of the solutions for the problems examined in the book.
Reviewer: Z.Dżygadło

MSC:

74E05 Inhomogeneity in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74J20 Wave scattering in solid mechanics
74A15 Thermodynamics in solid mechanics
74E30 Composite and mixture properties
80A20 Heat and mass transfer, heat flow (MSC2010)