Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/12889
Title: Conditions for strong ellipticity and M-eigenvalues
Authors: Qi, L 
Dai, HH
Han, D
Keywords: Elasticity tensor
M-eigenvalue
Strong ellipticity
Z-eigenvalue
Issue Date: 2009
Publisher: Higher Education Press
Source: Frontiers of mathematics in China, 2009, v. 4, no. 2, p. 349-364 How to cite?
Journal: Frontiers of mathematics in China 
Abstract: The strong ellipticity condition plays an important role in nonlinear elasticity and in materials. In this paper, we define M-eigenvalues for an elasticity tensor. The strong ellipticity condition holds if and only if the smallest M-eigenvalue of the elasticity tensor is positive. If the strong ellipticity condition holds, then the elasticity tensor is rank-one positive definite. The elasticity tensor is rank-one positive definite if and only if the smallest Z-eigenvalue of the elasticity tensor is positive. A Z-eigenvalue of the elasticity tensor is an M-eigenvalue but not vice versa. If the elasticity tensor is second-order positive definite, then the strong ellipticity condition holds. The converse conclusion is not right. Computational methods for finding M-eigenvalues are presented.
URI: http://hdl.handle.net/10397/12889
ISSN: 1673-3452
EISSN: 1673-3576
DOI: 10.1007/s11464-009-0016-6
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