Mechanics of composite materials. Textbook. (Mekhanika kompozitsionnykh materialov. Uchebnoe posobie). (Russian) Zbl 0555.73069

Pobedrya, B. E.

Moskva: Izdatel’stvo Moskovskogo Universiteta. 336 p. R. 0.90 (1984).

The monograph is devoted to micro and macro mechanics of composite materials, for small strains. Though it is the text of an advanced undergraduate course, the exposure presents the point of view of the author and of his collaborators and their contribution to the field.
A composite is defined as a mathematical model which is described with the help of discontinuities of the constitutive functions, with respect to material coordinates. There are nine chapters and six appendices.
The first chapter presents the basic formulation of the mechanics of continua, including elasticity, viscoelasticity and deformation theory of plasticity. The second chapter is devoted to the variational principles, the third one to the introduction of effective moduli and the constitutive equation formulated with the help of these moduli. Several simple one-dimensional examples (bar) are given in Ch. 4, 7 and 9. Laminar elastic composites are considered in Ch. 5, fibrous elastic composites in Ch. 6. Elastic-plastic composites are studied in Ch. 7 and the viscoelastic ones in Ch. 8. The last chapter is devoted to the propagation of waves.
The appendices present general informations concerning tensor calculus, curvilinear coordinates, Fourier transform, etc. No experimental data and methods are given. There are a great deal of proposed exercises. The literature is given after each chapter.
The reviewer considers the book to be a valuable one which would be worthwhile to be translated in English. Unfortunately, there are printing errors (even many blank pages).

Reviewer: N.Cristescu

MSC:

74E30	Composite and mixture properties
74-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74A40	Random materials and composite materials
74A20	Theory of constitutive functions in solid mechanics
74C99	Plastic materials, materials of stress-rate and internal-variable type
74D99	Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74J99	Waves in solid mechanics
74A99	Generalities, axiomatics, foundations of continuum mechanics of solids
74A60	Micromechanical theories
74M25	Micromechanics of solids

Keywords:

micro and macro mechanics; small strains; advanced undergraduate course; variational principles; effective moduli; Laminar elastic composites; fibrous elastic composites; Elastic-plastic composites