Asymptotic fields at frictionless and frictional cohesive crack tips in quasibrittle materials

Xiao, Q. Z.; Karihaloo, Bhushan Lal

doi:10.2140/jomms.2006.1.881

Cited by 34 publications

(38 citation statements)

References 39 publications

(41 reference statements)

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“…It is considered as an additional degree of freedom at relevant enrichment nodes in XFEM. We mention in passing that in [23] complete asymptotic expansions for frictionless and frictional cohesive cracks have been obtained which are analogous to the Williams expansions in brittle solids. These expansions are valid for many commonly used separation laws, e.g.…”

Section: Incremental-secant Modulus Iteration Scheme For Cohesive Cramentioning

confidence: 84%

“…Although only mode I problems are studied, extension of the scheme to mixed mode problems with or without friction is straightforward. The corresponding enrichment functions (counterparts of (7) and (8) for mode I) can be found in [23].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…For a pure mode I problem, the first term of the asymptotic displacement field at the tip of a cohesive crack corresponds to a non-integer eigenvalue that gives a normal displacement discontinuity over the cohesive-crack faces. It has been derived in [23] and is…”

Section: Incremental-secant Modulus Iteration Scheme For Cohesive Cramentioning

confidence: 99%

“…In this paper, we will use the leading term of the displacement asymptotic field at the tip of a cohesive crack in quasi-brittle materials obtained recently by Xiao and Karihaloo [23] as the crack tip enrichment function for the simulation of cracking or failure process using the XFEM. In the published literature (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Incremental‐secant modulus iteration scheme and stress recovery for simulating cracking process in quasi‐brittle materials using XFEM

Xiao

Karihaloo

Liu

2006

Numerical Meth Engineering

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SUMMARYIn this paper, an incremental-secant modulus iteration scheme using the extended/generalized finite element method (XFEM) is proposed for the simulation of cracking process in quasi-brittle materials described by cohesive crack models whose softening law is composed of linear segments. The leading term of the displacement asymptotic field at the tip of a cohesive crack (which ensures a displacement discontinuity normal to the cohesive crack face) is used as the enrichment function in the XFEM. The opening component of the same field is also used as the initial guess opening profile of a newly extended cohesive segment in the simulation of cohesive crack propagation. A statically admissible stress recovery (SAR) technique is extended to cohesive cracks with special treatment of non-homogeneous boundary tractions. The application of locally normalized co-ordinates to eliminate possible ill-conditioning of SAR, and the influence of different weight functions on SAR are also studied. Several mode I cracking problems in quasi-brittle materials with linear and bilinear softening laws are analysed to demonstrate the usefulness of the proposed scheme, as well as the characteristics of global responses and local fields obtained numerically by the XFEM.

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Section: Incremental-secant Modulus Iteration Scheme For Cohesive Cramentioning

confidence: 84%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Incremental-secant Modulus Iteration Scheme For Cohesive Cramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Incremental‐secant modulus iteration scheme and stress recovery for simulating cracking process in quasi‐brittle materials using XFEM

Xiao

Karihaloo

Liu

2006

Numerical Meth Engineering

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“…It is remarked, that this type of closure has also been observed in the experiments by Elssner et al (1994) and in the results of an analysis through discrete dislocations around a crack tip by Cleveringa et al (2000). Also, more recently, Xiao and Karihaloo (2006) using the Knein-Williams asymptotic technique, have shown that the crack faces of a pure mode I (frictionless) cohesive crack close in a cusp-like manner.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 53%

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

Gourgiotis¹,

Sifnaiou²,

Georgiadis³

2010

Recent Progress in the Mechanics of Defects

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Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s10704-010-9523-4Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics.

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A consistent partly cracked XFEM element for cohesive crack growth

Asferg

Poulsen

Nielsen

2007

Numerical Meth Engineering

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SUMMARYPresent extended finite element method (XFEM) elements for cohesive crack growth may often not be able to model equal stresses on both sides of the discontinuity when acting as a crack-tip element. The authors have developed a new partly cracked XFEM element for cohesive crack growth with extra enrichments to the cracked elements. The extra enrichments are element side local and were developed by superposition of the standard nodal shape functions for the element and standard nodal shape functions for a sub-triangle of the cracked element. With the extra enrichments, the crack-tip element becomes capable of modelling variations in the discontinuous displacement field on both sides of the crack and hence also capable of modelling the case where equal stresses are present on each side of the crack. The enrichment was implemented for the 3-node constant strain triangle (CST) and a standard algorithm was used to solve the non-linear equations. The performance of the element is illustrated by modelling fracture mechanical benchmark tests. Investigations were carried out on the performance of the element for different crack lengths within one element. The results are compared with previously obtained XFEM results applying fully cracked XFEM elements, with computational results achieved using standard cohesive interface elements in a commercial code, and with experimental results. The suggested element performed well in the tests.

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Asymptotic fields at frictionless and frictional cohesive crack tips in quasibrittle materials

Cited by 34 publications

References 39 publications

Incremental‐secant modulus iteration scheme and stress recovery for simulating cracking process in quasi‐brittle materials using XFEM

Incremental‐secant modulus iteration scheme and stress recovery for simulating cracking process in quasi‐brittle materials using XFEM

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

A consistent partly cracked XFEM element for cohesive crack growth

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