Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T20:02:34.510Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on sufficient symmetry conditions for isotropy of the elastic moduli tensor

Published online by Cambridge University Press:  31 January 2011

M.S. Dresselhaus  and
G. Dresselhaus
M.S. Dresselhaus
Affiliation:
Department of Electrical Engineering and Computer Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
G. Dresselhaus
Affiliation:
Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Group theoretical methods are used to obtain the form of the elastic moduli matrices and the number of independent parameters for various symmetries. Particular attention is given to symmetry groups for which 3D and 2D isotropy is found for the stress-strain tensor relation. The number of independent parameters is given by the number of times the fully symmetric representation is contained in the direct product of the irreducible representations for two symmetrical second rank tensors. The basis functions for the lower symmetry groups are found from the compatibility relations and are explicitly related to the elastic moduli. These types of symmetry arguments should be generally useful in treating the elastic properties of solids and composites.

Type
Articles
Information
Journal of Materials Research , Volume 6 , Issue 5 , May 1991 , pp. 1114 - 1118
Copyright
Copyright © Materials Research Society 1991

References

1Christensen, R. M., J. Appl. Mechanics 54, 772 (1987).CrossRefGoogle Scholar
2Rosen, B. W. and Shu, L. S., J. Composite Mater. 5, 279 (1971).CrossRefGoogle Scholar
3Levine, D., Lubensky, T. C., Ostlund, S., Ramaswamy, S., Steinhardt, P. J., and Toner, J., Phys. Rev. Lett. 54, 1520 (1985).CrossRefGoogle Scholar
4Steinhardt, P. J. and Ostlund, S., Physics of QuasiCrystals (World Scientific Publishing, Singapore, 1987), Chap. 6.CrossRefGoogle Scholar
5Koster, G. F., Dimmock, J., and Statz, H., Properties of the 32 point groups (MIT Press, Cambridge, MA, 1963).Google Scholar
6Tinkham, M., Group Theory (McGrawHill, New York, 1963).Google Scholar
7Kittel, C., Introduction to Solid State Physics (John Wiley and Sons, New York, 1953).Google Scholar
8Nye, J. F., Physical Properties of Crystals (Clarendon Press, Oxford, 1957).Google Scholar