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Mathematical Problems in Engineering
Volume 2013, Article ID 293861, 12 pages
Research Article

Explicit Dynamic Finite Element Method for Failure with Smooth Fracture Energy Dissipations

1Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA
2STUCKY Ltd., Rue du Lac 33, 1020 Renens VD 1, Switzerland
3Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA

Received 19 July 2013; Accepted 1 October 2013

Academic Editor: Timon Rabczuk

Copyright © 2013 Jeong-Hoon Song 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.


A numerical method for dynamic failure analysis through the phantom node method is further developed. A distinct feature of this method is the use of the phantom nodes with a newly developed correction force scheme. Through this improved approach, fracture energy can be smoothly dissipated during dynamic failure processes without emanating noisy artifact stress waves. This method is implemented to the standard 4-node quadrilateral finite element; a single quadrature rule is employed with an hourglass control scheme in order to decrease computational cost and circumvent difficulties associated with the subdomain integration schemes for cracked elements. The effectiveness and robustness of this method are demonstrated with several numerical examples. In these examples, we showed the effectiveness of the described correction force scheme along with the applicability of this method to an interesting class of structural dynamic failure problems.