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Mathematical Problems in Engineering
Volume 2015, Article ID 305397, 9 pages
Research Article

Deterministic and Probabilistic Investigation on Multiple Crack Interactions in a Semi-Infinite Domain

1Department of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, Republic of Korea
2Institute for Infrastructure Engineering, University of Western Sydney, Penrith, NSW 2751, Australia

Received 25 June 2015; Revised 15 July 2015; Accepted 22 July 2015

Academic Editor: Mohammed Nouari

Copyright © 2015 Eui-Keun Kim 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.


The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This study aims to investigate the interactions of multiple parallel cracks in a semi-infinite domain in both deterministic and probabilistic ways by using an automated finite element modeling procedure and the Monte Carlo simulation. The stress intensity factor is considered as an indicator of failure and accurately evaluated by using the domain integral technique. The variation of the stress intensity factor according to the position, the length, and the number of cracks is demonstrated. In a probabilistic investigation, the effects of the number of cracks, the random distribution of the crack lengths, and the crack interactions to the failure probability are studied for a semi-infinite domain. The stress redistribution among multiple cracks, the effect of unevenly distributed crack lengths, and the combined effect of crack length uncertainties and a crack shielding effect have been examined.