Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/13303
Title: Conditions for strong ellipticity of anisotropic elastic materials
Authors: Han, D
Dai, HH
Qi, L 
Keywords: Anisotropic materials
Copositivity
Elasticity tensors
Rhombic systems
Strong ellipticity
Z-eigenvalues
Issue Date: 2009
Source: Journal of elasticity, 2009, v. 97, no. 1, p. 1-13 How to cite?
Journal: Journal of Elasticity 
Abstract: In this paper, we derive necessary and sufficient conditions for the strong ellipticity condition of anisotropic elastic materials. We first observe that the strong ellipticity condition holds if and only if a second order tensor function is positive definite for any unit vectors. Then we further link this condition to the rank-one positive definiteness of three second-order tensors, three fourth-order tensors and a sixth-order tensor. In particular, we consider conditions of strong ellipticity of the rhombic classes, for which we need to check the copositivity of three second-order tensors and the positive definiteness of a sixth-order tensor. A direct method is presented to verify our conditions.
URI: http://hdl.handle.net/10397/13303
ISSN: 0374-3535
DOI: 10.1007/s10659-009-9205-5
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