Journal
JOURNAL OF ELASTICITY
Volume 97, Issue 1, Pages 1-13Publisher
SPRINGER
DOI: 10.1007/s10659-009-9205-5
Keywords
Elasticity tensors; Anisotropic materials; Strong ellipticity; Z-eigenvalues; Copositivity; Rhombic systems
Funding
- Research Grant Council of Hong Kong
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available