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Journal of Applied Mathematics
Volume 2013, Article ID 978026, 12 pages
Research Article

A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics

1Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
2Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, D-99423 Weimar, Germany
3Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam
4School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD 4001, Australia
5School of Engineering, Institute of Mechanics and Advanced Materials, Theoretical and Computational Mechanics, Cardiff University, Wales CF24 3AA, UK
6Department of Civil, Environmental & Architectural Engineering, Korea University, 5 Ga 1, An-Am Dong, Sung-Buk Gu, Seoul 136-701, Republic of Korea
7Aerospace Systems Ohio Eminent Scholar, University of Cincinnati, Cincinnati, OH 45221-0070, USA
8School of Civil, Environmental and Architectural Engineering, Korea University, 5 Ga 1, Anam-dong, Seongbuk-gu, Seoul 136-701, Republic of Korea

Received 15 January 2013; Accepted 1 May 2013

Academic Editor: Song Cen

Copyright © 2013 N. Vu-Bac 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.


This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.