A simplified mesh‐free method for shear bands with cohesive surfaces

Rabczuk, Timon; Areias, P.; Belytschko, Ted

doi:10.1002/nme.1797

Cited by 201 publications

(70 citation statements)

References 58 publications

(55 reference statements)

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“…In the first computation, we did not use adaptivity while in the second one, we allowed two refinement steps. The crack speed is shown in Figure 32 and agrees well with computations of other numerical studies, Rabczuk et al [43]; Belytschko et al [7]; Xu and Needleman [54]. The crack speed does not exceed the Rayleigh wave speed.…”

Section: Kalthoff Problemsupporting

confidence: 87%

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

2007

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This paper proposes a three dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modelled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results.Keywords extended element free Galerkin method (XEFG); three dimensional cracks; cohesive forces; static and dynamic fracture; extrinsic partition of unity enrichment; non-linear fracture mechanics.

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Section: Kalthoff Problemsupporting

confidence: 87%

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

2007

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“…While all previous meshfree approaches for fracture require crack path continuity, the cracking particles method [231][232][233][234][235] does not represent the crack as continuous surface. This makes the method particularly useful for 3D applications including complex crack patterns such as crack branching and crack coalescence.…”

Section: Cracking Particles Methodmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

162

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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“…We focus on the brittle failure pattern and an impact velocity of 17 m/s. The simulation of this problem had been reported by Belytschko et al [16], Menouillard et al [29], Rabczuk et al [41], Xu and Needleman [51], etc.…”

Section: Crack Branchingmentioning

confidence: 76%

A new crack tip element for the phantom‐node method with arbitrary cohesive cracks

Rabczuk

Gerstenberger

et al. 2008

Numerical Meth Engineering

220

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SUMMARYWe have developed a new crack tip element for the phantom node method. In this method, a crack tip can be placed inside an element. Therefore cracks can propagate almost independent of the finite element mesh. We developed two different formulations for the three-node triangular element and four-node quadrilateral element, respectively. Although this method is well suited for the one-point quadrature scheme, it can be used with other general quadrature schemes. We provide some numerical examples for some static and dynamic problems.

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A simplified mesh‐free method for shear bands with cohesive surfaces

Cited by 201 publications

References 58 publications

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

A new crack tip element for the phantom‐node method with arbitrary cohesive cracks

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