Abstract
A new approach to the generalized self-consistent method [1,2] has been developed for problems of the statistical mechanics of composites with composite or hollow inclusions. The approach can reduce the problem of predicting the effective elastic properties of composites to a simpler averaged problem of a single, composite, or hollow inclusion with inhomogeneous elastic surrounding in a homogeneous effective elastic medium. The problem of predicting the effective elastic properties of composites with unidirectional hollow fibers or hollow spherical inclusions are studied by using the new approach.
Similar content being viewed by others
References
A. A. Pan'kov, “Generalized self-consistent method for statistical mechanics of composite materials,” Mech. Compos. Mater.,33, No. 2, 112–118 (1997).
A. A. Pan'kov, “Analysis of effective elastic properties of composites with random structures by the generalized self-consistent method,” Izv. RAN Mekh. Tverd. Tela, No. 3, 68–76 (1997).
Yu. V. Sokolkin, A. M. Votinov, A. A. Tashkinov, A. M. Postnykh, and A. A. Chekalkin, Technology and Design of Carbon-Carbon Composites and Structures [in Russian], Nauka, Moscow (1996).
G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kiev (1985).
I. N. Frantsevich and D. M. Karpinos (eds.), Composite Materials of Fibrous Structure [in Russian], Naukova Dumka, Kiev (1970).
E. I. Grigolyuk and L. A. Fil'shtinskii, Perforated Plates and Shells [in Russian], Nauka, Moscow (1970).
T. D. Shermergor, Elasticity Theory of Micro-Nonhomogeneous Media [in Russian], Nauka, Moscow, (1977).
Composite Materials (8 volumes). Vol. 2 J. Sendetski (ed.), Mechanics of Composite Materials [in Russian], Mir, Moscow (1978).
R. M. Christensen, Mechanics of Composite Materials, John Wiley & Sons, New York (1979).
V. A. Kochetkov, “Calculation of characteristics of the elastic and thermophysical properties of a multi-phase composite containing composite or hollow spherical inclusions”, Mech. Compos. Mater.,30, No. 4, 371–377 (1994).
Yu. A. Dzenis and R. D. Maksimov, “Prediction of the physical-mechanical properties of hollow-sphere reinforced plastics,” Mech. Compos. Mater.,27, No. 3, 263–270 (1991).
V. A. Kochetkov, “Effective elastic characteristics and thermophysical properties of a unidirectional hybrid composite. Report 1,” Mech. Compos. Mater.,23, No. 1, 33–42 (1987).
R. Hill, “Theory of mechanical properties of fibrous composite materials,” Mekhanika [Russian translation],96, Moscow (1966).
V. I. Gorbachev, “Reduction problems for elastic space softened by a system of cylindrical pores,” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 63–67 (1983).
Additional information
Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.
Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 173–183, March–April, 1998.
Rights and permissions
About this article
Cite this article
Pan'kov, A.A. Generalized self-consistent method: Modeling and computation of effective elastic properties of composites with composite or hollow inclusions. Mech Compos Mater 34, 123–131 (1998). https://doi.org/10.1007/BF02256032
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02256032