Bounds on the effective elastic moduli of randomly oriented aggregates of hexagonal, trigonal, and tetragonal crystals are derived using the variational principles of Hashin and Shtrikman. The bounds are considerably narrower than the widely used Voigt and Reuss bounds. The Voigt‐Reuss‐Hill average lies within the Hashin‐Shtrikman bounds in nearly all cases. Previous bounds of Peselnick and Meister are shown to be special cases of the present results.
REFERENCES
1.
W. Voigt, Lehrbuch der Kristallphysik (Teubner, Leipzig, 1928).
2.
3.
J. P.
Watt
, G. F.
Davies
, and R. J.
O’Connell
, Rev. Geophys. Space Phys.
14
, 541
(1976
).4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
F. Birch, in Handbook of Physical Constants, edited by S. P. Clark, Jr. (The Geological Society of America, New York, 1966).
15.
H. Jeffreys, Cartesian Tensors (Cambridge U.P., Cambridge, 1961), p. 70.
16.
17.
18.
G. A.
Alers
and J. R.
Neighbours
, J. Phys. Chem. Solids
7
, 58
(1958
).19.
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© 1980 American Institute of Physics.
1980
American Institute of Physics
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