## Journal of Applied Mathematics

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

#### Abstract

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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 978026, 12 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808069

Digital Object Identifier
doi:10.1155/2013/978026

Mathematical Reviews number (MathSciNet)
MR3082126

Zentralblatt MATH identifier
1271.74418

#### Citation

Vu-Bac, N.; Nguyen-Xuan, H.; Chen, L.; Lee, C. K.; Zi, G.; Zhuang, X.; Liu, G. R.; Rabczuk, T. A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics. J. Appl. Math. 2013 (2013), Article ID 978026, 12 pages. doi:10.1155/2013/978026. https://projecteuclid.org/euclid.jam/1394808069

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