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Advances in Materials Science and Engineering
Volume 2015, Article ID 684065, 10 pages
Research Article

Implementation of Virtual Crack Closure Technique for Damaged Composite Plates Using Higher-Order Layerwise Model

1Department of Civil Engineering, Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea
2School of General Education, Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea

Received 5 January 2015; Revised 6 October 2015; Accepted 8 October 2015

Academic Editor: Ying Li

Copyright © 2015 Kwang S. Woo and Jae S. Ahn. 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.


A higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for single-edge-crack aluminum plates with patch repairs. The present method is based on -convergent approach and adopts the concept of subparametric elements. In assumed displacement fields, strain-displacement relations and three-dimensional constitutive equations of layers are obtained by combination of two- and one-dimensional shape functions. Thus, it allows independent implementation of -refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively. For verification of the present model, not only single-edge-crack plates but also V-notch aluminum plates are first analyzed. For patched aluminum plate with behavior of complexity, the accuracy and simplicity of the present model are shown with comparison of the results with previously published papers using the conventional three-dimensional finite elements based on -refinement.