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Technical Briefs

Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion

[+] Author and Article Information
B. R. Kim

Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, 335 Gwahangno, Yuseong-gu, Republic of Korea

H. K. Lee1

Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, 335 Gwahangno, Yuseong-gu, Republic of Korealeeh@kaist.ac.kr

1

Corresponding author.

J. Appl. Mech 77(2), 024503 (Dec 10, 2009) (5 pages) doi:10.1115/1.3197236 History: Received March 04, 2009; Revised May 31, 2009; Published December 10, 2009; Online December 10, 2009

With the help of the I-integrals expressed by Mura (1987, Micromechanics of Defects in Solids, 2nd ed., Martinus Nijhoff, Dordrecht) and the outward unit normal vector introduced by Ju and Sun (1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574), the closed form solution of the exterior-point Eshelby tensor for an elliptic cylindrical inclusion is derived in this work. The proposed closed form of the Eshelby tensor for an elliptic cylindrical inclusion is more explicit than that given by Mura, which is rough and unfinished. The Eshelby tensor for an elliptic cylindrical inclusion can be reduced to the Eshelby tensor for a circular cylindrical inclusion by letting the aspect ratio of the inclusion α=1. The closed form Eshelby tensor presented in this study can contribute to micromechanics-based analysis of composites with elliptic cylindrical inclusions.

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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Tensors
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Figures

Grahic Jump Location
Figure 1

A schematic description of an elliptic cylindrical inclusion embedded in an isotropic infinite body (cf. Ref. 2)

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