Modified Eshelby tensor for an anisotropic matrix with interfacial damage

TL;DR

This paper derives a simplified tensor algebraic expression for the modified Eshelby tensor in anisotropic matrices with interfacial damage, validated against finite element analysis for complex crystal structures.

Contribution

It introduces a new, simplified tensor algebraic formula for the modified Eshelby tensor considering interfacial damage in anisotropic materials.

Findings

Derived a simple tensor algebraic expression for the modified Eshelby tensor.

Validated the expression against finite element analysis for triclinic crystals.

Demonstrated applicability to complex anisotropic materials with interfacial damage.

Abstract

We derive a simple tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities (the 4th order identity tensor, the elastic stiffness tensor, and the Eshelby tensor) and two scalar quantities (the inclusion radius and interfacial spring constant), when the interfacial damage is modelled as a linear-spring layer of vanishing thickness. We validate the expression for a triclinic crystal involving 21 independent elastic constants against finite element analysis (FEA).