Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-20T09:39:13.185Z Has data issue: false hasContentIssue false
  • English
  • Français

On Invariants of Anisotropic Elasticity Constants

Published online by Cambridge University Press:  05 May 2011

Min-Zhong Wang  and
Bao-Sheng Zhao
Min-Zhong Wang*
Affiliation:
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
Bao-Sheng Zhao*
Affiliation:
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
*
*Professor
**Graduate student
Get access

Abstract

With the aid of a six-dimensional special eigenvector q, T.C.T.Ting finds five new invariants of anisotropic elasticity constants. The purpose of this paper is to consider some character of the eigenvector q. It is pointed that the six-dimensional special eigenvector q is unique, if it is independent of the coordinate transformation, and the general form of a three-rank orthogonal matrix is given if it has a three-dimensional special eigenvector like q. In addition, the concept of the special eigenvector q is extended and 20 invariants of anisotropic elasticity constants are obtained under rotation about x3-axis.

Keywords

InvariantsAnisotropicGauge notationEigenvector.
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 1 , March 2003 , pp. 185 - 190
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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

REFERENCES

1Ting, T. C. T., “Invariants of Anisotripic Elastic Constants,” Q. J. Mech. Appl. Math., 40, pp. 431–438 (1987).CrossRefGoogle Scholar
2Ting, T. C. T., Anisotripic Elasticity — Theory and Applications, Oxford University Press, Oxford, pp. 53–56 (1996).CrossRefGoogle Scholar
3Chen, S. T., “Construction of the Gauge Space of Anisotropic Elasticity Materials,” in Chinese, Acta Xian Traffic University, 17, pp. 117–124 (1983).Google Scholar
4Chen, S. T., “Some New Concepts of Elasticity and Its Application,” in Chinese, Acta Mechnica Sinica, 16, pp. 260–273 (1984).Google Scholar
5Mehrabadi, M. M. and Cowin, S. C., “Eigentensors of Linear Anisotropic Elastic Materials,” Q. J. Mech. Appl. Math., 43, pp. 15–39 (1990).CrossRefGoogle Scholar
6Wang, M. Z., “On the Inequalities Between the Stress and Strain Energy,” in Chinese, Acta Appl. Mech., 4, pp. 53–56 (1987).Google Scholar
7Mehrabadi, M. M., Cowin, S. C. and Horgan, C. O., “Strain Energy Density Bounds for Linear Anisotropic Elasticity,” J. Elasticity, 30, pp. 191–196 (1993).CrossRefGoogle Scholar