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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 947205, 10 pages
Research Article

Eigenstrain Boundary Integral Equations with Local Eshelby Matrix for Stress Analysis of Ellipsoidal Particles

1College of Sciences, Shanghai University, Shanghai 200444, China
2School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD 4001, Australia
3School of Engineering, Australian National University, Canberra, ACT 0200, Australia

Received 20 December 2013; Accepted 17 February 2014; Published 7 April 2014

Academic Editor: Yumin Cheng

Copyright © 2014 Hang Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.