With the aim of exploring extreme elastic properties, decompositions of the compliance tensor are established for various crystal classes. Representations are deduced that lead directly to well-structured forms for analyzing extreme properties. The properties of primary interest are the Lamé compliance and the axial compliance (reciprocal Young’s modulus). These exteme values and the corresponding directions play significant role in the study of those for the Poisson’s ratio, in particular the search for a negative minimum.
Love, A.E.H.A Treatise on the Mathematical Theory of Elasticity, 4th Edn., Reprint of the Cambridge University Press ( 1927), Dover, New York, 1944.
2.
Evans, K.E. and Alderson, K.L.Auxetic materials: functional materials and structures from lateral thinking. Advanced Materials, 12, 617-628 (2000).
3.
Scott N.H.An area modulus of elasticity: definition and properties. Journal of Elasticity, 58, 269-275 ( 2000).
4.
Kittinger, E., Tichý, J. and Bertagnolli , E.Example of a negative Poisson’s ratio. Physical Review Letters, 47, 712-714 (1981).
5.
Wheeler, L.T. and Guo, C.Y.Symmetry analysis of extreme areal Poisson ratio in anisotropic crystals. Journal of Mechanics of Materials and Structures, 2, 1471-1500 (2007).
6.
Walpole L.J.The elastic shear moduli of cubic crystal. Journal of Physics D: Applied Physics, 19, 457-462 (1986).
7.
Hayes, M. and Shuvalov, A.On the extreme values of Young’s modulus, the shear modulus and Poisson’s ratio for cubic materials. Journal of Applied Mechanics, 65, 786-787 (1998).
8.
Cazzani, A. and Rovati, M.Extrema of Young’s modulus for cubic and transversely isotropic solids. International Journal of Solids and Structures, 40, 1713-1744 (2003 ).
9.
Rovati, M.Directions of auxeticity for monoclinic crystals . Scripta Materialia, 51, 1087-1091 (2004 ).
10.
Ting, T.C.T.Anisotropic elastic constants that are structurally invariant. Quarterly Journal of Mechanics and Applied Mathematics , 53, 511-523 (2000).
11.
Ting, T.C.T.On anisotropic elastic materials for which Young’s modulus E (n) is independent of n or the shear modulus G(n, m) is independent of n and m. Journal of Elasticity, 81, 271-292 (2005).
12.
Ting, T.C.T.Explicit expression of the stationary values of Young’s modulus and the shear modulus for amisotropic elastic materials. Journal of Mechanics, 21, 171-182 (2005).
13.
Ting, T.C.T. and Barnett, D.M.Negative Poisson’s ratios in anisotropic linear elastic media. Journal of Applied Mechanics, 72, 929-931 (2005).
14.
Norris, A.N.Extreme values of Poisson’s ratio and other engineering moduli in anisotropic materials. Journal of Mechanics of Materials and Structures , 1, 793-812 (2006).
15.
Norris, A.N.Poisson’s ratio in cubic materials. Proc. R. Soc. A , 462, 3385-3405 (2006).
16.
Guo, C.Y. and Wheeler, L.T.Extreme Poisson’s Ratios and Related Elastic Crystal Properties. Journal of the Mechanics and Physics of Solids, 54, 690-707 (2006).
17.
Guo, C.Y. and Wheeler, L.T.Extreme Lamé compliance in anisotropic crystals. Mathematics and Mechanics of Solids, doi:10.1177/1081286507080807 (2008).
18.
Wheeler, L.Extreme Lamé compliance in crystals of trigonal symmetry-the case of α-quartz. Mathematics and Mechanics of Solids, DOI:10.1177/1081286508092607 (2008).
19.
Nye, J.F.Physical Properties of Crystals, Oxford University Press, Oxford, 1957 (reprinted 2000).
20.
Thomas, T.Y.On the stress-strain relations for cubic crystals . Proceedings of the National Academy of Sciences, U.S.A. , 55, 235-239 (1965).
21.
Walpole, L.J.Fourth-rank tensors of the thirty-two crystal classes: multiplication tables. Proceedings of the Royal Society of London A, 391, 149-179 (1984).
22.
Huntington, H.B.The Elastic Constants of Crystals, Academic, New York, 1958.
23.
Landolt, H.H. and Bornstein, R.Numerical Data and Functional Relationships in Science and Technology, III/29/a. Second and Higher Order Elastic Constants, Springer, Berlin, 1992.
