Extended meshfree methods without branch enrichment for cohesive cracks

Zi, Goangseup; Rabczuk, Timon; Wall, Wolfgang A.

doi:10.1007/s00466-006-0115-0

Cited by 174 publications

(59 citation statements)

References 50 publications

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“…Because of the cracks in the concrete, the displacement space of the standard EFG is enriched by the discontinuous displacement u e [27,34,35]. The displacement approximation for the concrete is given by…”

Section: A Methods For the Rigid Bond Using Lagrange Multipliersmentioning

confidence: 99%

A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures

Rabczuk

Bordas

et al. 2008

Engineering Fracture Mechanics

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287

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A three dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept and formulated for geometrically nonlinear problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. A cohesive zone model is used after crack initiation. The reinforcement modeled by truss or beam elements is connected by a bond model to the concrete. We applied the method to model the fracture of several reinforced concrete structures and compared the results to experimental data.

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Section: A Methods For the Rigid Bond Using Lagrange Multipliersmentioning

confidence: 99%

A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures

Rabczuk

Bordas

et al. 2008

Engineering Fracture Mechanics

Self Cite

287

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“…It was later extended to nonlinear materials and cohesive cracks by Rabczuk and Zi [227], Rabczuk et al [228]. In contrast to XFEM, due to the heavily overlapping shape functions, a crack tip enrichment has to be employed to ensure crack closure at the crack tip though alternative methods have been developed that avoid the use of tip enrichments [229,230]. However, those approaches are cumbersome in three dimensions.…”

Section: Extended Meshfreementioning

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

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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 refer among others to Dally (1979), Ravi-Chandar and Knauss (1984a,b), Knauss and Ravi-Chandar (1985), Ramulu and Kobayashi (1985), Fineberg et al (1991), Satoh (1996), Fineberg (1996, 1999), Fineberg and Marder (1999), and references therein, for a discussion of some experimental observations. Numerical simulations of the problem have been reported in Falk et al (2001), Klein et al (2001), Belytschko et al (2003), Zhou and Molinari (2004), Zhou et al (2005), Huespe et al (2006), Song et al (2006), Duarte et al (2007), Karedla and Reddy (2007), Remmers et al (2008), Zhang et al (2007), Zi et al (2007), to mention just a few references employing a variety of different numerical approaches.…”

Section: Crack Branching In Brittle Materialsmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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This paper presents the extension of some finite elements with embedded strong discontinuities to the fully transient range with the focus on dynamic fracture. Cracks and shear bands are modeled in this setting as discontinuities of the displacement field, the so-called strong discontinuities, propagating through the continuum. These discontinuities are embedded into the finite elements through the proper enhancement of the discrete strain field of the element. General elements, like displacement or assumed strain based elements, can be considered in this framework, capturing sharply the kinematics of the discontinuity for all these cases. The local character of the enhancement (local in the sense of defined at the element level, independently for each element) allows the static condensation of the different local parameters considered in the definition of the displacement jumps. All these features lead to an efficient formulation for the modeling of fracture in solids, very easily incorporated in an existing general finite element code due to its modularity. We investigate in this paper the use of this finite element formulation for the special challenges that the dynamic range leads to. Specifically, we consider the modeling of failure mode transitions in ductile materials and crack branching in brittle solids. To illustrate the performance of the proposed formulation, we present a series of numerical simulations of these cases with detailed comparisons with experimental and other numerical results reported in the literature. We conclude that these finite element methods handle well these dynamic problems, still maintaining the aforementioned features of computational efficiency and modularity.

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Extended meshfree methods without branch enrichment for cohesive cracks

Cited by 174 publications

References 50 publications

A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures

A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures

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

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

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