Revisiting the generalized self-consistent scheme in composites: Clarification of some aspects and a new formulation

Journal of the Mechanics and Physics of Solids

Volumn 56, Issue 10, 2008, Pages 2984-3002

  Benveniste, Y ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Composite material; Inhomogeneous material; Particulate reinforced material

Indexed keywords

ALUMINUM METALLURGY; ANTENNA LOBES; COMPOSITE MATERIALS; VOLUME FRACTION;

EFFECTIVE SHEAR MODULUS; GENERALIZED SELF-CONSISTENT SCHEMES; HOMOGENEOUS BOUNDARY CONDITION; INHOMOGENEOUS MATERIALS; MATRIX-BASED COMPOSITES; MICRO MECHANICS MODEL; MULTIPHASE COMPOSITES; PARTICULATE REINFORCED MATERIALS;

PARTICLE REINFORCED COMPOSITES;

EID: 55349146238     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2008.06.006     Document Type: Article

References (32)

1. Benveniste, Y., 1985. The effective mechanical behaviour of composite materials with imperfect contact between the constituents. Mech. Mater. 4, 197-208.
2. Benveniste, Y., 1986. On the effective thermal conductivity of multiphase composites. J. Appl. Math. Phys. (ZAMP) 37, 696-713.
3. Benveniste, Y., 1987. A new approach to the application of Mori-Tanaka theory in composite materials. Mech. Mater. 6, 147-157.
4. Bruggeman, D.A.G., 1935. Berechnung verschiedener physikalicher Konstanten von heterogen Substanzen, I Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. (German) [Calculation of various physical constants in heterogeneous substances. I. Dielectric constants and conductivity of composites from isotropic substances.]. Ann. Phys. 24, 636-670.
5. Budiansky, B., 1965. On the elastic moduli of some heterogeneous materials, J. Mech. Phys. Solids 13, 223-227.
6. Christensen, R.M., 1979. Mechanics of Composite Materials. Wiley, New York.
7. Christensen, R.M., 1990. A critical evaluation for a class of micromechanics models. J. Mech. Phys. Solids 38, 379-404.
8. Christensen, R.M., 1998. Two theoretical elasticity models. J. Elast. 50, 15-25.
9. Christensen, R.M., Lo, K.H., 1979. Solutions for effective and shear properties in three phase and cylinder models. J. Mech. Phys. Solids 27, 315-330 (see also, erratum in J. Mech. Phys. Solids 34 (1986) 639).
10. Hashin, Z., 1962. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29, 143-150.
11. Hashin, Z., 1968. Assessment of the self-consistent scheme approximation: conductivity of particulate composites, J. Compos. Mater. 2, 284-289.
12. Hashin, Z., 1980. Thermoelastic properties and conductivity of carbon/carbon fiber composites. Mech. Mater. 8, 293-308.
13. Hashin, Z., 1983. Analysis of composite materials - a survey. J. Appl. Mech. 50, 481-505.
14. Hashin, Z., Shtrikman, S., 1962. A variational approach to the theory of the effective magnetic permeability of multiphase composites, J. Appl. Phys. 33, 3125-3131.
15. Hashin, Z., Shtrikman, S., 1963. A variational approach to the theory of the elastic behaviour of multiphase composites. J. Mech. Phys. Solids 11, 127-140.
16. Hill. R., 1965. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213-222.
17. Huang. Y., Hu, H.X., 1995. A generalized self-consistent mechanics method for solids containing elliptical inclusions. J. Appl. Mech., Trans. ASME 62, 566-572.
18. Jiang, B., Weng, G.J., 2004. A generalized self-consistent polycrystal model for the yield strength of nanocrystalline materials. J. Mech. Phys. Solids 52, 1125-1149.
19. Jiang, C.P., Tong, Z.H., Cheung, Y.K., 2003. A generalized self-consistent method accounting for fiber section shape. Int. J. Solids Struct. 40, 2589-2609.
20. Kerner. E.H., 1956a. The electrical conductivity of composite media. Proc. Phys. Soc. B 69, 802-807.
21. Kerner, E.H., 1956b. The elastic and thermo-elastic properties of composite media. Proc. Phys. Soc. B 69, 808-813.
22. Mackenzie, J.K., 1950. The elastic constants of a solid containing spherical holes. Proc. Phys. Soc. B 63, 2-11.
23. McCartney, N.L., Kelly, A., 2008. Maxwell's far-field methodology applied to the predicyion of properties of multi-phase isotropic particulate composites. Proc. R. Soc. A 464, 423-446.
24. Miloh, T., Benveniste, Y., 1988. A generalized self-consistent scheme for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies. J. Appl. Phys. 63, 789-796.
25. Milton. C.W., 1981. Concerning bounds on the transport and mechanical properties of multicomponent composite materials. Appl. Phys. A 26, 125-130.
26. Mori, T., Tanaka, K., 1973. Average stress in matrix and average energy of materials with misfitting inclusions. Acta Metall. 21, 571-574.
27. Riccardi, A., Montheillet. F., 1999. A generalized self-consistent method for solids containing randomly oriented spheroidal inclusions. Acta Mech. 133, 39-56.
28. Roscoe, R., 1952. The viscosity of suspensions of rigid spheres. Br. J. Appl. Phys. 3, 267-269.
29. Siboni, G., Benveniste, Y., 1991. A micromechanics model for the effective thermomechanical behaviour of multi-phase composite media. Mech. Mater. 11, 107-122.
30. Walpole, L.J., 1966. On bounds for the overall elastic moduli of inhomogeneous systems-l. J. Mech. Phys. Solids 14, 151-162.
31. Weng, G.J., 1984. Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci. 22, 845-856.
32. Weng, G.J., 1990. The theoretical connection between Mori-Tanaka theory and the Hashin-Shtrikman-Walpole bounds. Int. J. Eng. Sci. 28, 1111-1120.