Inproceedings,
Implementation of the edge-based smoothed extended finite element method
Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) Vienna, Austria, September 10-14, 2012, page 8117--8123. European Community on Computational Methods in Applied Sciences (ECCOMAS), (September 2012)
Abstract
Cutting is an essential manipulation task in surgery. For these and other discontinuities T. Belytschko et al. introduced the Extended Finite Element Method (XFEM), that allows the simulation of cuts, cracks or interfaces in virtual environments. To reduce the high computational costs in FE simulations and to improve the accuracy, G.R. Liu et al. developed the Smoothed Finite Element Method (SFEM). Combining these two methods results in the Smoothed Extended Finite Element Method (SXFEM) which was first introduced by St.P.A. Bordas et al.. They used the cell-based strain smoothing with triangular and quadrangular elements to show the ability for FE simulations. In this paper we describe our implementation of the edge-based SXFEM in the large FE software Code Aster of Electricit´e de France SA. These elements can be implemented easily because they only require the modification of the discretized gradient operator B. The implementation works for linear problems, e.g. problems with material interfaces, discretized with linear triangular elements. We compare the simulation results obtained by this method with those obtained with the standard XFEM using triangular elements. The principle of strain smoothing extended to the partition of unity enrichment simplifies the numerical integration of discontinuous approximations in the XFEM.
