Error estimation for crack simulations using the XFEM

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OriginalspracheEnglisch
Seiten (von - bis)1459-1474
Seitenumfang16
FachzeitschriftInternational Journal for Numerical Methods in Engineering
Jahrgang91
Ausgabenummer13
PublikationsstatusVeröffentlicht - 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.

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Error estimation for crack simulations using the XFEM. / Prange, C.; Loehnert, S.; Wriggers, P.
in: International Journal for Numerical Methods in Engineering, Jahrgang 91, Nr. 13, 28.08.2012, S. 1459-1474.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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T1 - Error estimation for crack simulations using the XFEM

AU - Prange, C.

AU - Loehnert, S.

AU - Wriggers, P.

PY - 2012/8/28

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