TY  - JOUR
A1  - Chen, Lei
A1  - Rabczuk, Timon
A1  - Liu, G.R.
A1  - Zeng, K.Y.
A1  - Kerfriden, Pierre
A1  - Bordas, Stéphane Pierre Alain
T1  - Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
JF  - Computer Methods in Applied Mechanics and Engineering
N2  - This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting “edge-based” smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, “super-convergence” and “ultra-accurate” solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction.
KW  - Angewandte Mathematik
KW  - Strukturmechanik
Y1  - 2012
U6  - http://dx.doi.org/10.1016/j.cma.2011.08.013
ER  - 
TY  - JOUR
A1  - Nguyen-Xuan, Hung
A1  - Liu, G.R.
A1  - Bordas, Stéphane Pierre Alain
A1  - Natarajan, S.
A1  - Rabczuk, Timon
T1  - An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
JF  - Computer Methods in Applied Mechanics and Engineering
N2  - An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
KW  - Angewandte Mathematik
KW  - Strukturmechanik
Y1  - 2013
SP  - 252
EP  - 273
ER  -