Details
| Original language | English |
|---|---|
| Pages (from-to) | 1459-1474 |
| Number of pages | 16 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 91 |
| Issue number | 13 |
| Publication status | Published - 28 Aug 2012 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- General Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 91, No. 13, 28.08.2012, p. 1459-1474.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Error estimation for crack simulations using the XFEM
AU - Prange, C.
AU - Loehnert, S.
AU - Wriggers, P.
PY - 2012/8/28
Y1 - 2012/8/28
N2 - 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.
AB - 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.
KW - Cracks
KW - Error estimation
KW - XFEM
UR - http://www.scopus.com/inward/record.url?scp=84865539298&partnerID=8YFLogxK
U2 - 10.1002/nme.4331
DO - 10.1002/nme.4331
M3 - Article
AN - SCOPUS:84865539298
VL - 91
SP - 1459
EP - 1474
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 13
ER -