Properties of the Eshelby tensor and existence of the equivalent ellipsoidal inclusion solution

We show that the Eshelby tensor, SE, when written in the 6 × 6 matrix (Voigt) form, is weakly positive definite, i.e., it can be written as a product of two positive definite matrices. All eigenvalues of SE are real and lie between 0 and 1, for an arbitrary anisotropic elastic medium with a positive...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2018-12, Vol.121 (C), p.71-80
Main Authors: Barnett, D.M., Cai, Wei
Format: Article
Language:English
Subjects:
Anisotropy
Eigenvalues
Elastic anisotropy
Elastic media
Equivalence
Eshelby tensor
Eshelby’s inclusion
Inhomogeneity
Invertibility
Materials elasticity
Materials Science
Mathematical analysis
Matrix
Matrix methods
Mechanics
Physics
Stiffness
Stress state
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that the Eshelby tensor, SE, when written in the 6 × 6 matrix (Voigt) form, is weakly positive definite, i.e., it can be written as a product of two positive definite matrices. All eigenvalues of SE are real and lie between 0 and 1, for an arbitrary anisotropic elastic medium with a positive definite elastic stiffness tensor C. The weakly positive definiteness property leads to a direct proof of the existence of Eshelby’s equivalent inclusion solution for a “transformed” ellipsoidal inhomogeneity in an infinite elastic medium.
ISSN:0022-5096
1873-4782
DOI:10.1016/j.jmps.2018.07.019