An improvement of the EDI method in linear elastic fracture mechanics by means of an <i>a posteriori</i> error estimator in <i>G</i>

Giner, Eugenio; Fuenmayor, F. J.; Tarancón, J. E.

doi:10.1002/nme.889

Cited by 9 publications

(10 citation statements)

References 50 publications

(103 reference statements)

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“…The square of the error in the energy norm is related to the error in strain energy and therefore to the error in the strain energy release rate G and the error in the SIFs [36]:…”

Section: Contact Problemmentioning

confidence: 99%

An Abaqus implementation of the extended finite element method

Giner

Sukumar

Tarancón

et al. 2009

Engineering Fracture Mechanics

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323

175

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In this paper, we introduce an implementation of the extended finite element method for fracture problems within the finite element software ABAQUS TM . User subroutine (UEL) in Abaqus is used to enable the incorporation of extended finite element capabilities. We provide details on the data input format together with the proposed user element subroutine, which constitutes the core of the finite element analysis; however, pre-processing tools that are necessary for an X-FEM implementation, but not directly related to Abaqus, are not provided. In addition to problems in linear elastic fracture mechanics, non-linear frictional contact analyses are also realized. Several numerical examples in fracture mechanics are presented to demonstrate the benefits of the proposed implementation.

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“…The square of the error in the energy norm is related to the error in strain energy and therefore to the error in the strain energy release rate G and the error in the SIFs [36]:…”

Section: Contact Problemmentioning

confidence: 99%

An Abaqus implementation of the extended finite element method

Giner

Sukumar

Tarancón

et al. 2009

Engineering Fracture Mechanics

Self Cite

323

175

View full text Add to dashboard Cite

show abstract

“…A common strategy to determine the finite element approximation u N,h ∈ W N,h of the nonlinear discrete variational problems (13) and (14) is to apply the iterative Newton-Raphson algorithm which we sketch here briefly, since virtually the same technique will be applied in the error analysis in Sect. 3.…”

Section: Finite Element Discretizations In Computationalmentioning

confidence: 99%

“…For further details see Giner et al [13], Heintz et al [16], Rüter and Stein [29,30], Stein et al [36] and Xuan et al [40].…”

Section: Introductionmentioning

confidence: 97%

On the duality of finite element discretization error control in computational Newtonian and Eshelbian mechanics

Rüter¹,

Stein

2006

Comput Mech

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In this paper, goal-oriented a posteriori error estimators of the averaging type are presented for the error obtained while approximately evaluating the J-integral in nonlinear elastic fracture mechanics. Since the value of the J-integral is one component of the material force acting on the crack tip of a pre-cracked elastic body, the appropriate mechanical framework to be chosen is the one named after Eshelby rather than classical Newtonian mechanics. However, in a finite element setting, the discretized Eshelby problem is generally not solved explicitly. Rather, its solution is approximated by the finite element solution of the corresponding discretized dual Newton problem. As a consequence, discrete material forces arise not only at the crack tip but also at other nodes of the current finite element mesh. It is the objective of this paper to establish goal-oriented a posteriori error estimators in both the framework of Eshelbian and Newtonian mechanics and to elaborate their dual relations. This allows to control the error of the J-integral while, at the same time, no further discrete material forces arise during the adaptive mesh refinement process which could lead to misleading mechanical interpretations of the results obtained by the finite Dedicated to the memory of the esteemed colleague Professor Karl Popp, University of Hannover, who unexpectedly passed away on April 24, 2005. M. Rüter (B)

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“…In recent years, goal-oriented error estimates have also been developed and succesfully applied to the field of fracture mechanics, see [9,10,17,18,19,24,27]. Remarkably, the first steps in this direction had already been taken in 1984 by Babuška and Miller [3].…”

Section: Introductionmentioning

confidence: 97%

Goal-Oriented Error Estimates Based on Different FE-Spaces for the Primal and the Dual Problem with Applications to Fracture Mechanics

Rüter¹,

Korotov²,

Steenbock³

2006

Comput Mech

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The objective of this paper is to derive goal-oriented a posteriori error estimators for the error obtained while approximately evaluating the nonlinear J -integral as a fracture criterion in linear elastic fracture mechanics (LEFM) using the finite element method. Such error estimators are based on the well-established technique of solving an auxiliary dual problem. In a straightforward fashion, the solution to the discretized dual problem is sought in the same FEspace as the solution to the original (primal) problem, i.e. on the same mesh, although it merely acts as a weight of the discretization error only. In this paper, we follow the strategy recently proposed by Korotov et al. [J Numer Math 11:33-59, 2003; Comp Lett (in press)] and derive goal-oriented error estimators of the averaging type, where the discrete dual solution is computed on a different mesh than the primal solution. On doing so, the FE-solutions to the primal and the dual problems need to be transferred from one mesh to the other. The necessary algorithms are briefly explained and finally some illustrative numerical examples are presented.

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An improvement of the EDI method in linear elastic fracture mechanics by means of an a posteriori error estimator in G

Cited by 9 publications

References 50 publications

An Abaqus implementation of the extended finite element method

An Abaqus implementation of the extended finite element method

On the duality of finite element discretization error control in computational Newtonian and Eshelbian mechanics

Goal-Oriented Error Estimates Based on Different FE-Spaces for the Primal and the Dual Problem with Applications to Fracture Mechanics

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