A robust implementation of Zienkiewicz and Zhu's local patch recovery method

Labbé, Paul; Garon, André

doi:10.1002/cnm.1640110507

Cited by 22 publications

(16 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, if complete first-order polynomials were used for the stress recovery, as these polynomials have three unknown coefficients, at least three integration points should be used in each integration subdomain. Labbe and Garon [35] used this procedure in a FEM framework to overcome the difficulties associated with using SPR in patches containing few elements.…”

Section: Assembly Of Patchesmentioning

confidence: 99%

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

Ródenas

González‐Estrada

Tarancón

et al. 2008

Numerical Meth Engineering

107

View full text Add to dashboard Cite

SUMMARYA 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.

show abstract

Section: Assembly Of Patchesmentioning

confidence: 99%

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

Ródenas

González‐Estrada

Tarancón

et al. 2008

Numerical Meth Engineering

107

View full text Add to dashboard Cite

show abstract

“…The advent of Zienkiewicz and Zhu's estimator instigated a healthy discussion on the best approach to a posteriori error estimation. From that point forward, two general strategies have been established: the so-called residual estimators, based on Babuška-type strategies [132,134], and indicators based on projection/smoothing, after Zienkiewicz and Zhu's technique [133,[135][136][137][138]. Marusich and Ortiz (1995) [53] used the plastic work rate in each element in order to refine the finite element mesh in cutting simulations.…”

Section: Error and Distortion Metricsmentioning

confidence: 99%

Modelling and Simulation of Machining Processes

Vaz

Owen

Kalhori

et al. 2007

Arch Computat Methods Eng

View full text Add to dashboard Cite

The modelling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. The present work outlines the wide range of complex physical phenomena involved in the chip formation in a descriptive manner. In order to improve and understand the process different numerical strategies have been used for simulation. Several of these numerical strategies are reviewed and a short discussion of their relative merits and drawbacks is presented. By means of several examples, where a combined experimental/numerical effort was undertaken, we try to illustrate what numerical techniques, models and pertinent parameters are needed for successful simulations.

show abstract

“…Their method is based on the use of unstructured calculation grids adapted to increase the accuracy of coherent structures. At each node, the gradients of the displacement fields are determined with the help of a reconstruction method used in the finite element and finite volume methods [8][9][10][11]. The gradients are obtained at a node by a weighted sum of the gradients calculated on the adjacent elements sharing this node.…”

Section: Introductionmentioning

confidence: 99%