Rigorous bounds on the effective thermal conductivity of composites with ellipsoidal inclusions

International Journal of Engineering Science

Volumn 48, Issue 4, 2010, Pages 417-428

  Wu, Linzhi ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Composites; Effective thermal conductivity; Ellipsoidal inclusions; Transition layer; Upper and lower bounds

Indexed keywords

COMPLEMENTARY ENERGY; COMPLEX INTEGRALS; EFFECTIVE THERMAL CONDUCTIVITY; ELLIPSOIDAL INCLUSIONS; GEOMETRIC PARAMETER; INTERFACE CONDITIONS; LOWER BOUNDS; MINIMUM POTENTIAL ENERGY; MULTI-POINT CORRELATIONS; TEMPERATURE FIELD; TRANSITION LAYERS; UPPER AND LOWER BOUNDS; UPPER BOUND; VARIATIONAL PRINCIPLES;

HEAT FLUX; THERMAL CONDUCTIVITY; THERMOANALYSIS; VARIATIONAL TECHNIQUES;

INCLUSIONS;

EID: 76749168969     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2009.11.003     Document Type: Article

References (21)

1. Batchelor G.K. Transport properties of two-phase materials with random structure. Annual Review of Fluid Mechanics 6 (1974) 227-255
2. Beran M.J., and Molyneux J. Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media. Quarterly of Applied Mathematics 24 (1966) 107-118
3. Brown Jr. W.F. Dielectric constants, permeabilities, and conductivities of random media. Transactions of the Society of Rheology 9 (1965) 357-380
4. Bruno O.P. The effective conductivity of strongly heterogeneous composites. Proceedings of the Royal Society of London A 433 (1991) 353-381
5. Elsayed M.A. Bounds for effective thermal, electrical, and magnetic properties of heterogeneous materials using high order statistical information. Journal of Mathematical Physics 15 11 (1974) 2001-2015
6. Francfort G.A., and Murat F. Homogenization and optimal bounds in linear elasticity. Archive for Rational Mechanics and Analysis 94 (1986) 307-334
7. Hashin Z., and Shtrikman S. A variational approach to the theory of the effective magnetic permeability of multiphase materials. Journal of Applied Physics 33 (1962) 3125-3131
8. Hashin Z. The elastic moduli of heterogeneous materials. ASME Journal of Applied Mechanics 29 (1962) 143-150
9. Hashin Z. On elastic behaviour of fiber reinforced materials of arbitrary transverse phase geometry. Journal of the Mechanics and Physics of Solids 13 (1965) 119-134
10. Hashin Z. Analysis of composite materials - a survey. ASME Journal of Applied Mechanics 55 (1983) 481-505
11. Hori M. Statistical theory of effective electrical, thermal and magnetic properties of random heterogeneous materials. I. Perturbation expansions for the effective permittivity of cell materials. Journal of Mathematical Physics 14 (1973) 514-523
12. Hori M. Statistical theory of effective electrical, thermal and magnetic properties of random heterogeneous materials. II. Bounds for the effective permittivity of statistically anisotropic materials. Journal of Mathematical Physics 14 (1973) 1942-1949
13. Kantor Y., and Bergman D.J. Improved rigorous bounds on the effective elastic moduli of a composite material. Journal of the Mechanics and Physics of Solids 32 (1984) 41-62
14. Keller J.B., Rubenfeld L.A., and Molyneux J.E. Extremum principles for slow viscous flows with applications to suspensions. Journal of Fluid Mechanics 30 (1967) 97-125
15. Milton G.W., and Phan-Thien N. New bounds on the effective moduli of two component materials. Proceedings of the Royal Society of London A 380 (1982) 305-331
16. McCoy J.J. Recent Advances in Engineering Science vol. 5 (1970), Gordon and Breach, New York
17. Pham D.C. Bounds on the effective properties of some multiphase matrix mixtures of coated-sphere geometry. Mechanics of Materials 27 (1998) 249-260
18. Phan-Thien N., and Milton G.W. New bounds on the effective thermal conductivity of N-phase materials. Proceedings of the Royal Society of London A 380 (1982) 333-348
19. Sen A.K., and Torquato S. Effective conductivity of anisotropic two-phase composite media. Physics Review B 39 (1989) 4504-4515
20. Torquato S. Random heterogeneous media: microstructure and improved bounds on effective properties. Applied Mechanics Review 44 2 (1991) 37-76
21. Willis J.R. Bounds and self-consistent estimates for the overall moduli of anisotropic composites. Journal of Mechanics and Physics of Solids 25 (1977) 185-202