Abstract
A method for determining the effective elastic constants and the factors of stress concentration in microstructural elements is proposed for nonlinear incompressible multicomponent composite materials randomly reinforced with spheroidal inclusions with an arbitrary ratio of the longitudinal and lateral dimensions. Use is made of the Mori-Tanaka scheme that has, as a first approximation, the result of calculation of the elastic characteristics based on a model taking account of two-point statistical moment functions of arbitrarily high order.
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References
V. V. Bolotin,Life of Machines and Structures [in Russian], Mashinostroyeniye, Moscow (1990).
B. P. Maslov, “The nonlinear elastic properties of stochastically nonuniform media,”Prikl. Mekh.,9, No. 8, 91–95 (1973).
B. P. Maslov, “Macroscopic elastic moduli of the third order,”Prikl. Mekh.,15, No. 7, 57–61 (1979).
B. P. Maslov, “Effective constants in the theory of geometrically nonlinear solids,”Prikl. Mekh.,17, No. 5, 45–50 (1981).
B. P. Maslov, “The reduced constants of composite materials with initial strains of components,”Prikl. Mekh.,17, No. 9, 57–63 (1981).
B. P. Maslov, “The stress-strain state in a matrix of stochastically reinforced composites,”Mekh. Komp. Mater., No. 3, 396–402 (1989).
B. P. Maslov, Ya. Ya. Rushchitskii, and A. P. Kovalenko, “Complete sets of physical constants of the nonlinear microstructural theory of a two-phase elastic mixture for some structural materials,”Prikl. Mekh.,32, No. 4, 18–26 (1996).
A. N. Guz', L. P. Khoroshun, and G. A. Vanin,Mechanics of Materials, Vol. 1 of the three-volume seriesMechanics of Composite Materials and Structural Elements [in Russian], Naukova Dumka, Kiev (1982).
L. P. Khoroshun, B. P. Maslov, E. N. Shikula, and L. V. Nazarenko,Statistical Mechanics and the Effective Properties of Materials, Vol. 3 of the 12-volume seriesMechanics of Composites (A. N. Guz', editor general) [in Russian], Naukova Dumka, Kiev (1993).
L. P. Khoroshun and B. P. Maslov,The Nonlinear Properties of Composite Materials with a Stochastic Structure [in Russian], Naukova Dumka, Kiev (1993).
A. N. Guz, “Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 1. Problem statement and general relationships,”Prikl. Mekh.,34, No. 12, 3–16 (1998) (Int. Appl. Mech.,34, No. 12, 1175–1186 (1998)).
Z. Hashin, “Analysis of composite materials,”J. Appl. Mech.,50, No. 9, 481–505 (1983).
T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions,”Acta Metallurgica,21, No. 4, 571–574 (1973).
J. R. Willis, “Elasticity theory of composites,” in:Mechanics of Solids (H. G. Hopkins and M. J. Sewell, eds.), Pergamon Press (1982), pp. 653–686.
J. R. Willis, “On methods for bounding the overall properties of nonlinear composites,”J. Mech. Phys. Solids,39, No. 1, 73–86 (1991).
Additional information
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 108–114, March, 2000.
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Maslov, B.P. Stress concentration in incompressible multicomponent materials. Int Appl Mech 36, 384–390 (2000). https://doi.org/10.1007/BF02681922
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DOI: https://doi.org/10.1007/BF02681922