Smoothed extended finite element method for continua

Sundararajan Natarajan (1) , Stefano Dal Pont (2) , Marc Duflot (3) , Timon Rabczuk (4) , Stéphane Bordas (1)

1 University of Glasgow
2 LCPC/BCC - Division Bétons et Composites cimentaires
3 Cenaero
4 Bauhaus-Universität Weimar

The extended finite element method (XFEM) introduced by Belytschko [1] allows discontinuities to be arbitrarily present in the domain, i.e, discontinuities can be independent of the mesh. However this complicates the numerical integration of the stiffness matrix, because it requires sub-division of elements cut by discontinuity, which in 3D may be computationally costly. In this paper, we address this issue by proposing a new method named as the Smoothed eXtended Finite Element Method (SmXFEM) [2]. This method combines the strain smoothing technique proposed by Liu et al., [3] for finite element method, coined as Smoothed Finite Element Method (SFEM) with the XFEM. The SmXFEM shares the properties of both the SFEM [4] and XFEM. The SmXFEM alleviates the need to compute the derivative of shape functions and numerical integration of singular functions, commonly encountered in linear elastic fracture mechanics. This is achieved by transforming the surface integration to line integration along the boundary of an element. The effectiveness of the method is illustrated by a few benchmark examples taken from linear elastic fracture mechanics. The results obtained with SmXFEM compare well with those of the standard XFEM.

Mots clés: METHODE DES ELEMENTS FINIS; MECANIQUE DE LA RUPTURE

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Sundararajan Natarajan, Stefano Dal Pont, Marc Duflot, Timon Rabczuk, Stéphane Bordas. Smoothed extended finite element method for continua. Colloque national en calcul des structures, May 2009, France. 6p. ⟨hal-00402569⟩