Methods of theory of random functions in problems of macroscopic properties of microinhomogeneous media

V. V. Bolotin and V. N. Moskalenko, ?Macroscopic thermal conductivity and diffusion coefficients in microinhomogeneous solids,? Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 7?13 (1967).

V. V. Bolotin and V. N. Moskalenko, ?Problem of determining the elastic constants of a microinhomogeneous medium,? Zh. Prikl. Mekh. Tekh. Fiz., No. 1, 66?72 (1968).

G. A. Van Fo Fy, Theory of Reinforced Materials [in Russian], Naukova Dumka, Kiev (1971).

S. D. Volkov and V. Ya. Dolgikh, ?Structural stresses in reinforced plates,? Mekh. Polim., No. 3, 413?420 (1967).

S. D. Volkov, V. P. Stavrov, V. Ya. Dolgikh, and V. M. Mendel'son, ?Initial thermostructural stresses in two-component media,? Dokl. Akad. Nauk SSSR,183, No. 1 53?55 (1968).

I. M. Gel'fand and G. E. Shilov, Generalized Functions and Operations on Them [in Russian], Fizmatgiz, Moscow (1958).

G. A. Ermakov, A. G. Fokin, and T. D. Shermergor, ?Effective moduli of materials reinforced with an anisotropic fibers,? Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 110?117 (1974).

V. D. Kindzheri, Measurements at High Temperatures [in Russian], Metallurgizdat, Moscow (1963).

M. A. Krivoglaz and A. S. Cherevko, ?On elastic moduli of solid mixtures,? Fiz. Met. Metalloved., No. 2, 161?165 (1959).

I. M. Lifshits and L. N. Rozentsbeig, ?Toward the theory of elastic properties of polycrystals,? Zh. Éksp. Teor. Fiz., No. 11, 967?980 (1946).

V. A. Lomakin, ?On deformation of microinhomogeneous elastic bodies,? Prikl. Mat. Mekh., No. 5, 888?893 (1965).

V. A. Lomakin, ?The effect of microinhomogeneities of structure of materials on their mechanical properties,? in: Reliability Problems in Structural Mechanics [in Russian], Vilnius (1968), pp. 107?112.

V. A. Lomakin, Statistical Problems of Mechanics of Deformable Solids [in Russian], Nauka, Moscow (1970).

B. P. Maslov, ?Nonlinear elastic properties of stochastically inhomogeneous media,? Prikl. Mekh.,9, No. 8, 91?95 (1973).

B. P. Maslov, ?Nonlinear creep of stochastically inhomogeneous media,? Prikl. Mekh.,10, No. 10, 64?69 (1974).

B. P. Maslov, ?Elastoplastic deformation of materials strengthened by fibers,? Prikl. Mekh.,10, No. 11, 116?119 (1974).

B. P. Maslov and L. P. Khoroshun, ?Effective characteristics of elastic, physically nonlinear inhomogeneous media,? Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 149?154 (1977).

A. Kh. Melikbekyan, ?Thermoelastic constants of layered composites of multidirectional reinforcement,? Prikl. Mekh.,11, No. 8, 33?40 (1975).

S. I. Meshkov and A. V. Chigarev, ?Deformation of highly isotropic composite media,? Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 63?67 (1976).

G. N. Savin and L. P. Khoroshun, ?Statistically isotropic deformation of composite materials,? Dopov. Akad. Nauk UkrRSR, No. 9, 804?808 (1967).

G. N. Savin and L. P. Khoroshun, ?Problem of elastic constants of randomly reinforced materials,? Mechanics of Continuous Media and Related Problems of Analysis [in Russian], Nauka, Moscow (1972), pp. 437?444.

V. P. Stavrov, V. Ya. Dolgikh, and S. D. Volkov, ?Elastic constants of randomly reinforced plates,? Mekh. Polim., No. 2, 259?265 (1967).

A. G. Fokin, ?Singular approximation in the computation of elastic properties of reinforced systems,? Mekh. Polim., No. 3, 502?506 (1973).

A. G. Fokin and T. D. Shermergor, ?Elastic moduli of textured materials,? Inzh. Zh., Mekh. Tverd. Tela, No. 1, 129?133 (1967).

A. G. Fokin and T. D. Shermergor, ?Computation of effective elastic moduli of composition materials taking account of multiparticle interactions,? Zh. Prikl. Mekh. Tekh. Fiz., No. 1, 51?57 (1969).

A. G. Fokin and T. D. Shermergor, ?Dielectric constant of inhomogeneous materials,? Zh. Tekh. Fiz.,39, No. 7, 1308?1315 (1969).

A. G. Fokin and T. D. Shermergor, ?Elastic and rheological characteristics of fibrous composition materials,? Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 123?129 (1973).

L. P. Khoroshun, ?Some problems of correlation theory of structurally inhomogeneous elastic bodies,? Mekh. Polim., No. 3, 365?371 (1966).

L. P. Khoroshun, ?Thermoelastic properties of randomly reinforced media,? Prikl. Mekh.,2, No. 9, 99?106 (1966).

L. P. Khoroshun, ?Toward a theory of isotropic deformation of elastic bodies with random inhomogeneities,? Prikl. Mekh.3, No. 9, 12?19 (1967).

L. P. Khoroshun, ?A method of determining elastic moduli of reinforced bodies,? Mekh. Polim., No. 1, 78?85 (1968).

L. P. Khoroshun, ?Statistical theory of deformation of unidirectional fibrous materials,? Prikl. Mekh.,4, No. 7, 8?15 (1968).

L. P. Khoroshun, ?Elastic properties of materials reinforced by unidirectional short fibers,? Prikl. Mekh.,8, No. 12, 86?92 (1972).

L. P. Khoroshun, ?Prognosis of thermoelastic properties of materials reinforced by unidirectional discrete fibers,? Prikl. Mekh.,10, No. 12, 23?30 (1974).

L. P. Khoroshun and B. P. Maslov, ?Effective moduli of elasticity for bodies weakaned by oriented fissures,? Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10, 924?927 (1976).

L. P. Khoroshun, A. Kh. Melikbekyan, and S. A. Mokhbaliev, ?Toward a theory of deformation of composites of multidirectional random reinforcement,? Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10, 917?919 (1974).

L. P. Khoroshun, A. Kh. Melikbekyan, and V. M. Pinchuk, ?Prognosis of properties of disoriented fibrous composites,? Prikl. Mekh.,12, No. 12, 13?19 (1976).

T. D. Shermergor and A. G. Fokin, ?Use of the theory of random functions for determining the limits of effective elastic moduli of reinforced materials,? in: Reliability Problems in Structural Mechanics [in Russian], Vilnius (1968), pp. 133?138.

Z. Hashin and S. A. Strikman, ?A variational approach to the theory of the elastic behavior of multiphase materials,? J. Mech. Phys. Solids,11, No. 2 127?140 (1963).

R. A. Hill, ?A self-consistent mechanics of composite materials,? J. Mech. Phys. Solids,13, No. 4, 213?222 (1965).

E. Kröner, ?Elastic moduli of perfectly disordered composite material,? J. Mech. Phys. Solids,15, No. 5, 319?324 (1967).

A. Reuss, ?Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung,? Z. Angew. Math. Mech.,9, No. 1, 49?58 (1929).

W. Voigt, Lehrbuch der Kristallphysik, Johnson Reprint Corporation (1910), p. 234.