New estimates for macroscopic elastic moduli of random polycrystalline aggregates

Philosophical Magazine

Volumn 86, Issue 2, 2006, Pages 205-226

  Chinh, P D ^a  

^a GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Viet Nam)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL ORIENTATION; ELASTIC MODULI; SINGLE CRYSTALS;

AGGREGATES ELASTIC MODULI; MACROSCOPIC MODULI;

POLYCRYSTALLINE MATERIALS;

EID: 30344432433     PISSN: 14786435     EISSN: 14786443     Source Type: Journal    
DOI: 10.1080/14786430500343876     Document Type: Article

References (45)

1. W. Voigt, Lehrbuch der Krystallphysik (Teuber, Leizig, 1928).
2. A. Reuss, Z. Angew. Math. Mech. 9 49 (1929).
3. D.A.G. Bruggeman, Annal Phys. (Leipzig) 24 636 (1935).
4. R. Landauer, in Electrical Transport and Optical Properties of Inhomogeneous Media, edited by J.C. Garland and D.B. Tanner (AIP, New York, 1978).
5. E. Kröner, J. Engng Mech. Div. 106 889 (1980).
6. G.W. Milton, Commun. Math. Phys. 99 463 (1985).
7. A.N. Norris, Mech. Mater. 4 1 (1985).
8. D.C. Pham, J. Phys. Condensed Matter 10 9729 (1998).
9. D.C. Pham and N. Phan-Thien, Int. J. Engng Sci. 36 273 (1998).
10. D.C. Pham, Phys. Rev. B 64 104205 (2001).
11. D.C. Pham, Physica B 334 98 (2003).
12. D.C. Pham and S. Torquato, J. Appl. Phys. 94 6591 (2003).
13. R. Hill, Proc. Phys. Soc. A 65 349 (1952).
14. Z. Hashin and S. Shtrikman, J. Mech Phys. Solids 10 343 (1962).
15. D.C. Pham, Int. J. Engng Sci. 31 11 (1993).
16. D.C. Pham, Arch. Rational Mech. Anal. 127 191 (1994).
17. D.C. Pham, Phil. Mag. A 76 31 (1997).
18. D.C. Pham, J. Appl. Phys. 88 1346 (2000).
19. M.J. Beran, Statistica Continuum Theories (Wiley, New York, 1968).
20. M.N. Miller, J. Math. Phys. 10 1988 (1969).
21. R. Zeller and P.H. Dederichs, Phys. Stat. Sol(b) 55 831 (1973).
22. M.A. Elsayed, J. Math. Phys. 15 2001 (1974).
23. T.D. Sermergor, Theory of Elasticity of Micro-Inhomogeneous Media (Nauka, Moscow, 1977).
24. M.W.M. Williemse and W.J. Caspers, J. Math. Phys. 20 1824 (1979).
25. J.J. McCoy, in Mechanics Today, edited by S. Nemat-Nasser, Vol. 6 (Pergamon Press, Oxford and New York, 1981).
26. N. Phan-Thien and G.W. Milton, Q. Appl. Math. 41 59 (1983).
27. J. Helsing, Proc. R. Soc. A 444 363 (1994).
28. D.C. Pham, Int. J. Solids Struct. 33 1745 (1996).
29. S. Torquato, Random Heterogeneous Media (Springer, New York, 2002).
30. I.I. Sirotin and M.P. Saskolskaia, Fundamentals of Crystallophysics (Nauka, Moscow, 1979).
31. W.A. Wooster, Application of Tensors and Thoery of Groups for Description of Physical Properties of Crystals (Mir, Moscow, 1977).
32. M. Hamermesh, Group Theory and its Application to Physical Problems (Addition-Wesley, London, 1964).
33. D.C. Pham, J. Appl. Phys. 80 2253 (1996b).
34. R.L. Weaver, J. Mech. Phys. Solids 38 55 (1990).
35. Landolt-Börnstein, Group III: Crystal and Solid State Physics, Vol. 11 (Springer-Verlag, Berlin, 1979).
36. D.C. Pham and S. Torquato, J. Appl. Phys. 97 013535 (2005).
37. H.H. Warra, H. Koch and E. Kröner, J. Mater. Sci. Soc. Japan 14 131 (1977).
38. M.J. Silva, N.C. Hayes and L.J. Gibson, Int. J. Mech. Sci. 37 1161 (1995).
39. K. Li, X.L. Gao and G. Subhash, Int. J. Solids Struct. 42 1777 (2005).
40. M. Ostoja-Starzewski and J. Schulte, Phys. Rev. B 54 278 (1996).
41. K. Schulgasser, J. Phys. C 10 407 (1977).
42. G.W. Milton and R.V. Kohn, J. Mech. Phys. Solids 36 597 (1988).
43. M. Avellaneda and G.W. Milton, SIAM J. Appl. Math. 49 824 (1989).
44. S. Ahmed and R.B. Thomson, J. Acoust. Soc. Am. 99 2086 (1996).
45. J.A. Turner, J. Acoust. Soc. Am. 106 541 (1999).