Error estimation for crack simulations using the XFEM

authored by: C. Prange, S. Loehnert, P. Wriggers
Abstract: The extended finite element method (XFEM) is by now well-established for crack calculations in linear elastic fracture mechanics. An advantage of this method is its discretization independence for crack simulations. Nevertheless, discretization errors occur when using the XFEM. In this paper, a simple recovery based error estimator for the discretization error in XFEM-calculations for cracks is presented. The method is based on the Zienkiewicz and Zhu error estimator. Enhanced smoothed stresses incorporating the discontinuities and singularities because of the cracks are recovered to enable the error estimation for arbitrary distributed cracks. This approach also allows the consideration of materials with generally inelastic behaviour. The enhanced stresses are computed by means of a least square fit problem. To assess the quality of the error estimator, global norms and the effectivity index for the global energy norm for examples with known analytical solutions are presented.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 91
Pages: 1459-1474
No. of pages: 16
ISSN: 0029-5981
Publication date: 28.08.2012
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, General Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.4331 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{a66f122565f84a919f37273884d34738,
title = "Error estimation for crack simulations using the XFEM",
abstract = "The extended finite element method (XFEM) is by now well-established for crack calculations in linear elastic fracture mechanics. An advantage of this method is its discretization independence for crack simulations. Nevertheless, discretization errors occur when using the XFEM. In this paper, a simple recovery based error estimator for the discretization error in XFEM-calculations for cracks is presented. The method is based on the Zienkiewicz and Zhu error estimator. Enhanced smoothed stresses incorporating the discontinuities and singularities because of the cracks are recovered to enable the error estimation for arbitrary distributed cracks. This approach also allows the consideration of materials with generally inelastic behaviour. The enhanced stresses are computed by means of a least square fit problem. To assess the quality of the error estimator, global norms and the effectivity index for the global energy norm for examples with known analytical solutions are presented.",
keywords = "Cracks, Error estimation, XFEM",
author = "C. Prange and S. Loehnert and P. Wriggers",
year = "2012",
month = aug,
day = "28",
doi = "10.1002/nme.4331",
language = "English",
volume = "91",
pages = "1459--1474",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "13",
}