Clausius-Mossotti-type approximation for elastic moduli of a cubic array of spheres

Physical Review B - Condensed Matter and Materials Physics

Volumn 68, Issue 2, 2003, Pages

  Cohen, Israel ^a   Bergman, David J ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ARTICLE; CALCULATION; MATHEMATICAL MODEL; SHEAR STRESS; TECHNIQUE; YOUNG MODULUS;

EID: 0141482172     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.68.024104     Document Type: Article

References (20)

1. Y. Kantor and D.J. Bergman, J. Mech. Phys. Solids 30, 355 (1982).
2. Y. Kantor and D.J. Bergman, Appl. Phys. Lett. 41, 932 (1982).
3. Z. Hashin and S. Shtrikman, J. Mech. Phys. Solids 11, 127 (1963).
4. K.C. Nunan and J.B. Keller, J. Mech. Phys. Solids 32, 259 (1984).
5. S. Nemat-Nasser and M. Taya, Q. Appl. Math. 39, 43 (1981).
6. S. Nemat-Nasser, T. Iwakuma, and M. Hejazi, Mech. Mater. 1, 239 (1982).
7. S. Torquato, J. Mech. Phys. Solids 45, 1421 (1997).
8. S. Torquato, J. Mech. Phys. Solids 46, 1411 (1998).
9. Y. Kantor and D.J. Bergman, J. Mech. Phys. Solids 32, 41 (1984).
10. D.J. Bergman, in, Les Méthodes de l’Homogénéisation: Théorie et Application en Physique, edited by R. Dautray (Eyrolles, Paris, 1985), p. 1.
11. P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Pt. 1, Chap. 7, p. 884.
12. D.J. Bergman, Phys. Rev. B 19, 2359 (1979).
13. J.D. Eshelby, Proc. R. Soc. London, Ser. A 241, 376 (1957).
14. N.W. Ashcroft and N.D. Mermin, Solid State Physics (Holt, New York, 1976), p. 539.
15. R.C. McPhedran and G.W. Milton, Appl. Phys. A: Solids Surf. 26, 207 (1981).
16. I. Cohen and D.J. Bergman, J. Mech. Phys. Solids 51, 1433 (2003).
17. B.U. Felderhof and P.L. Iske, Phys. Rev. A 45, 611 (1992).
18. I.S. Sokolnikoff, Mathematical Theory of Elasticity, 2nd ed. (McGraw-Hill, New York, 1956), Chap. 6, p. 343.
19. A.K. Mal and S.J. Singh, Deformation of Elastic Solids (Prentice-Hall, New Jersey, 1991), Chap. 6, p. 182.
20. P.M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Pt. 2, Chap. 13, p. 1807.