Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-19T08:20:30.602Z Has data issue: false hasContentIssue false
  • English
  • Français

The Stationary Values of Young's Modulus For Monoclinic and Triclinic Materials

Published online by Cambridge University Press:  05 May 2011

T. C. T. Ting
T. C. T. Ting*
Affiliation:
Division of Mechanics and Computation, Stanford University, Durand 262, Stanford, CA 94305–4040, U.S.A.
*
* Consulting Professor, also Professor Emeritus of University of Illinois at Chicago
Get access

Abstract

The stationary values (maximum, minimum, saddle point) of Young modulus E(n) for a general anisotropic elastic materials is studied. The general results are then spcialized for monoclinic materials. Equations that provide the direction n for a stationary value are given. Some have an explicit solution. Other may require a numerical computation. The equations that required numerical solutions are two coupled polynomials of degree no more than four.

Keywords

Anisotropic elasticityYoung's modulusTriclinic materials, Monoclinic materials
Type
Articles
Information
Journal of Mechanics , Volume 21 , Issue 4 , December 2005 , pp. 249 - 253
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Lempriere, B. M., “Poisson's Ratio in Orthotropic Materials,” AMA Journal, 6(11), pp. 2226–2227 (1968).Google Scholar
2.Turley, J. and Sines, G., “The Anisotropy of Young's Modulus, Shear Modulus and Poisson's Ratio in Cubic Materials,” J. Phys., D(4), pp. 264–271 (1971).Google Scholar
3.Li, Y., “The Anisotropic Behavior of Poisson's Ratio, Young's Modulus, and Shear Modulus in Hexagonal Materials,” Phys. Stat. Sol., (a)38, pp. 171–175 (1976).CrossRefGoogle Scholar
4.Theocaris, P. S. and Philippidis, T. P., “True Bounds on Poisson's Ratios for Transversely Isotropic Solids,” J. Strain Analysis, 27(1), pp. 43–44 (1992).CrossRefGoogle Scholar
5.Boulanger, Ph. and Hayes, M., “Poisson's Ratio for Orthotropic Materials,” J. Elasticity, 50, pp. 87–89 (1998).CrossRefGoogle Scholar
6.Hayes, M. and Shuvalov, A., “On the Extreme Values of Young's Modulus, the Shear Modulus, and Poisson's Ratio for Cubic Materials,” J. Appl. Mech., 65, pp. 786–787 (1998).CrossRefGoogle Scholar
7.Zheng, Q. S. and Chen, T. Y., “New Perspective on Poisson's Ratios of Elastic Solids,” Acta Mech., 150, pp. 191–195 (2001).CrossRefGoogle Scholar
8.Cazzani, A. and Rovati, M., “Extrema of Young's Modulus for Cubic and Transversely Isotropic Solids,” Int. J. Solids Structures, 40, pp. 1713–1744 (2003).CrossRefGoogle Scholar
9.Cazzani, A. and Rovati, M., “Extrema of Young's Modulus for Elastic Solids with Tetragonal Symmetry,” Int. J. Solids Structures, 42, pp. 5057–5096 (2005).CrossRefGoogle Scholar
10.Ting, T. C. T. and Chen, T. Y., “Poisson's Ratio for Anisotropic Elastic Materials Can Have no Bounds,” Q. J. Mech. Appl. Math., 58(1), pp. 73–82 (2005).CrossRefGoogle Scholar
11.Ting, T. C. T., “Very Large Poison's Ratio with a Bounded Transverse Strain in Anisotropic Elastic Materials,” J. Elasticity, 77(2), pp. 163–176 (2004).CrossRefGoogle Scholar
12.Ting, T. C. T., and Barnett, D. M., “Negative Poisson's Ratios in Anisotropic Linear Elastic Media,” J. Appl. Mech., 72, pp. 929–931 (2005).CrossRefGoogle Scholar
13.Ting, T. C. T., “Explicit Expression of the Stationary Values of Young's Modulus and the Shear Modulus for Anisotropic Elastic Materials,” J. of Mechanics (formerly the Chinese Journal of Mechanics-Series A), 21(4), pp. 255–266 (2005).CrossRefGoogle Scholar
14.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,” J. Elasticity, 82(1), in press (2006).Google Scholar
15.Saint-Venant, B., “Memoire sur la Distribution des Elasticies,” J. Math. Pures er Appl. (Liouville) II, 10, pp. 297–349 (1863).Google Scholar
16.Ravinovich, A. L., “On the Elastic Constants and Strength of Aircraft Materials,” Trudy Trentrs. Aero-gidvodin., 582, pp. 1–56 (1946).Google Scholar
17.Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, Holden-Day, San Francisco (1963).Google Scholar
18.Ting, T. C. T., Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York (1996).CrossRefGoogle Scholar
19.Sirotin, Yu. I. and Shakol'skaya, M. P., Fundamentals of Crystal Physics, MIR Pub., Moscow (1982).Google Scholar
20.Voigt, W., Lehrbuch der Kristallphysik, Leipzig (1910).Google Scholar
21.Kolodner, I. I., “Existence of Longitudinal Waves in Anisotorpic Media,” J. Acoust. Soc. Am., 40, pp. 730–731 (1966).CrossRefGoogle Scholar
22.Cowin, S. C. and Mehrabadi, M. M., “Anisotropic Symmetries of Linear Elasticity,” Appl. Mech. Review, 48(5), pp. 247–285 (1995).CrossRefGoogle Scholar
23.Ting, T. C. T., “Anisotropic Elastic Constants that are Structurally Invariant,” Q. J. Mech. Appl. Math., 53(4), pp. 511–523 (2000).CrossRefGoogle Scholar
24.Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, University Press, Cambridge (1927).Google Scholar
25.Nye, J. F., Physical Properties of Crystals, Clarendon Press, Oxford (1985).Google Scholar
26.Chadwick, P., Vianello, M. and Cowin, S. C., “A New Proof that the Number of Linear Elastic Symmetries is Eight,” J. Mech. Phys. Solids, 49, pp. 2471–2492 (2001).CrossRefGoogle Scholar
27.Ting, T. C. T., “Generalized Cowin-Mehrabadi Theorems and a Direct Proof that the Number of Linear Elastic Symmetries is Eight,” Int. J. Solids Structure, 40, pp. 7129–7142 (2003).CrossRefGoogle Scholar