A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting

Rodenas, J. J., Gonzalez Estrada, Octavio Andres, Tarancon, J. E. and Fuenmayor, F. J. 2008. A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting. International Journal for Numerical Methods in Engineering 76 (4) , pp. 545-571. 10.1002/nme.2313

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Abstract

A new stress recovery procedure that provides accurate estimations of the discretization error for linear elastic fracture mechanic problems analyzed with the extended finite element method (XFEM) is presented. The procedure is an adaptation of the superconvergent patch recovery (SPR) technique for the XFEM framework. It is based on three fundamental aspects: (a) the use of a singular+smooth stress field decomposition technique involving the use of different recovery methods for each field: standard SPR for the smooth field and reconstruction of the recovered singular field using the stress intensity factor K for the singular field; (b) direct calculation of smoothed stresses at integration points using conjoint polynomial enhancement; and (c) assembly of patches with elements intersected by the crack using different stress interpolation polynomials at each side of the crack. The method was validated by testing it on problems with an exact solution in mode I, mode II, and mixed mode and on a problem without analytical solution. The results obtained showed the accuracy of the proposed error estimator.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords:	extended finite element method; error estimation; superconvergent patch recovery; singular stress field; linear elastic fracture mechanics
ISSN:	0029-5981
Last Modified:	19 Mar 2016 23:17
URI:	https://orca.cardiff.ac.uk/id/eprint/45998

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