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

By Juan José Ródenas, Octavio Andrés González-Estrada, J. E. Tarancón, F. Fuenmayor. 2008

107 citations recorded by the source corpus.

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. Copyright © 2008 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d96f749f706b2d5399ff0aead933e4d1da5c708a

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Efficient finite element methodology based on cartesian grids: application to structural shape optimization (2013, methodology): “” However in the XFEM framework, where the mesh is independent of the crack, efficient recovery techniques have been already proposed based on theMoving Least Squares (MLS) technique [44–47] and some on the SPR technique [42, 48], which introduce worthy improvements to the solution specially along t”
Strain smoothing in FEM and XFEM (2010, unknown): “[20] as well as [77].”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, background): “This flexibility simplifies local adaptive processes, as the regenerated mesh need not conform to the crack faces [19–21] does not come for free, as (1) numerical integration requires special attention [22–24]; (2) optimal convergence requires enriching a volume independent of the mesh size, thereby”
Extended finite element method with global enrichment (2015, methodology): “In standard XFEM those higher order terms can be represented by the FE part of the approximation, in addition since the 13 Page 13 of 81 http://mc.manuscriptcentral.com/nme International Journal for Numerical Methods in Engineering Peer Review O nly tip enrichment functions are weighted by the FE sh”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “Such error estimation tools for the X-FEM have been designed, for example, see Rodenas et al. (2008) and Duﬂot and Bordas (2008).”