Phase-interchange relations for the elastic moduli of two-phase composites

International Journal of Engineering Science

Volumn 34, Issue 7, 1996, Pages 739-760

  Gibiansky, L V ^a   Torquato, S ^a  

^a Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041621259     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7225(95)00130-1     Document Type: Article

References (42)

1. J. B. KELLER, J. Math. Phys. 5, 548 (1964).
2. K. S. MENDELSON, J. Appl. Phys. 46, 917 (1975).
3. A. M. DYKHNE, Soviet J. Exp. Theor. Phys. 7, 110 (1970) (in Russian); Soviet Phys. JETP 32, 63 (1971).
4. A. M. DYKHNE, Soviet J. Exp. Theor. Phys. 7, 110 (1970) (in Russian); Soviet Phys. JETP 32, 63 (1971).
5. G. W. MILTON, J. Appl. Phys. 52, 5294 (1981).
6. A. V. CHERKAEV and L. V. GIBIANSKY, Proc. R. Soc. Edinburgh 122A, 93 (1992).
7. D. J. BERGMAN, Phys. Rep. C 43, 377 (1988).
8. M. AVELLANEDA, A. V. CHERKAEV, K. A. LURIE and G. W. MILTON, J. Appl. Phys. 63, 4989 (1988).
9. K. SCHULGASSER, J. Math. Phys. 17, 378 (1976).
10. V. NESI, J. Math. Phys. 32, 2263 (1991).
11. O. BRUNO, Commun. Pure Appl. Math XLII, 769 (1990).
12. V. L. BERDICHEVSKY, Variational Principle of Continuum Mechanics (in Russian). Nauka, Moscow (1983).
13. J. HELSING, G. W. MILTON and A. B. MOVCHAN, submitted to J. Mech. Phys. Solids.
14. L. V. GIBIANSKY and S. TORQUATO, J. Mech. Phys. Solids 43, 1587 (1995).
15. K. A. LURIE and A. V. CHERKAEV, Proc. R. Soc. Edinburgh A 99, 71 (1984).
16. K. A. LURIE and A. V. CHERKAEV, Proc. R. Soc. Edinburgh A 104, 21 (1986).
17. F. MURAT and L. TARTAR, Calcul des Variations et Homogeneisation. Les Methodes de l' Homogeneisation: Theorie et Applications en Physique, Vol. 57, Coll. de la Dir. des Etudes et Recherches de Electr. de France, Eyrlles, Paris, 319-370 (1985).
18. L. TARTAR, Ennio de Giorgi Colloquium (Edited by P. Kree) Pitman Research Notes in Mathematics Vol. 125, pp. 168-187 (1985).
19. A. V. CHERKAEV and L. V. GIBIANSKY, J. Mech. Phys. Solids 41, 937 (1993).
20. L. V. GIBIANSKY and G. W. MILTON, Proc. R. Soc. Lond. A 440, 163 (1993).
21. L. V. GIBIANSKY and S. TORQUATO, Trans. Phil. Soc. 353, 243 (1995).
22. L. V. GIBIANSKY and S. TORQUATO, Proc. R. Soc. Lond. A 452, 253 (1996).
23. G. W. MILTON, Composite Media and Homogenization Theory (Edited by G. Dal Maso and G. Dal Antonio), vol. 5, Progress in Non-linear Differential Equations and their Applications, series (Edited by H. Brezis), pp. 223. Birkhauser, Boston (1991).
24. G. W. MILTON, Phys. Rev. Lett. 46, 542 (1981).
25. G. W. MILTON, J. Mech. Phys. Solids 30, 177 (1982).
26. Z. HASHIN, J. Mech. Phys. Solids 13, 119 (1965).
27. M. AVELLANEDA and G. W. MILTON, SIAM J. Appl. Math. 49, 824 (1989).
28. M. RUDELSON, Master Degree thesis, St. Petersburg Technical University, St. Petersburg, Russia (1989).
29. N. SILNUTZER, Ph.D. thesis, University of Pennsylvania, Philadelphia (1972).
30. Z. HASHIN and S. SHTRIKMAN, J. Mech. Phys. Solids 11, 127 (1963).
31. L. J. WALPOLE, J. Mech. Phys. Solids 14, 151 (1966).
32. MAPLE V Release 2, Princeton University, Copyright (c) 1981-1992 by the University of Waterloo.
33. G. FRANCFORT and F. MURAT, Non-Classical Continuum Mechanics (Edited by R. Knops and A. A. Lacey) pp. 197. Cambridge University Press, Cambridge (1987).
34. K. SCHULGASSER, J. Appl. Phys. 47, 1880 (1976).
35. G. W. MILTON and N. PHAN-THIEN, Proc. R. Soc. Lond. A 380, 305 (1982).
36. A. R. DAY, K. A. SNYDER, E. J. GARBOCZI and M. F. THORPE, J. Mech. Phys. Solids 40, 1031 (1992).
37. J. CHEN, L. C. DAVIS and M. F. THORPE, J. Appl. Phys. 77, 4349 (1995).
38. M. F. THORPE, J. CHEN, and I. M. JASIUK, Proc. IUTAM Symp. on Microstructure-Property Interactions in Composite Materials (Edited by R. Pyrz), pp. 361-373. Kluwer, Dordrecht (1995).
39. I. M. JASIUK, Int. J. Solids Struct. 32, 407 (1995).
40. R. HILL, J. Mech. Phys. Solids 12, 199 (1964).
41. L. V. BERLYAND and S. M. KOZLOV, Arch. Rat. Mech. Anal. 118, 95 (1992).
42. R. HILL, J. Mech. Phys. Solids 11, 357 (1963).