Evaluation of the Eshelby tensor for polygonal inclusions

The Eshelby tensor field is evaluated analytically for polygonal inclusions of arbitrary shape. The formula contributed in the paper is directly expressed as function of the coordinates defining the vertices of the polygon, thus avoiding the use of complex variables and anomalies exploited in previo...

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Bibliographic Details
Published inComposites. Part B, Engineering Vol. 115; pp. 170 - 181
Main Authors Trotta, S., Marmo, F., Rosati, L.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 15.04.2017
Subjects
Analytical modelling
Micro-mechanics
Nano-structures
Particle-reinforcement
Nano-structures
Micro-mechanics
Analytical modelling
Particle-reinforcement
Online AccessGet full text
ISSN1359-8368
1879-1069
DOI10.1016/j.compositesb.2016.10.018

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Summary:The Eshelby tensor field is evaluated analytically for polygonal inclusions of arbitrary shape. The formula contributed in the paper is directly expressed as function of the coordinates defining the vertices of the polygon, thus avoiding the use of complex variables and anomalies exploited in previous contributions on the subject. It has been obtained by evaluating analytically the displacement field induced by a uniform eigenstrain within the inclusion and differentiating its expression in order to derive the infinitesimal strain tensor and, hence, the Eshelby tensor. This allows us to deal only with the first derivative of the Green tensor, appearing in the expression of the displacement field, rather than addressing its second derivative as commonly done in the literature. The proposed formulation has been implemented in a Matlab code and we report the numerical results concerning inclusions whose boundary is defined by Laurent polynomials or by quasi-circular shapes.
ISSN:1359-8368
1879-1069
DOI:10.1016/j.compositesb.2016.10.018