Application of Particle Methods to Static Fracture of Reinforced Concrete Structures

Rabczuk, Timon; Belytschko, Ted

doi:10.1007/s10704-005-3075-z

Cited by 195 publications

(68 citation statements)

References 41 publications

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“…The wider the crack opens, the smaller are the bond stresses. A more detailed description of the bond model is given in Rabczuk and Belytschko [35].…”

Section: Non-planar Crack Growthmentioning

confidence: 99%

A three-dimensional large deformation meshfree method for arbitrary evolving cracks

Rabczuk

Belytschko

2007

Computer Methods in Applied Mechanics and Engineering

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263

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A new approach for modelling discrete cracks in meshfree particle methods in three dimensions is described. The cracks can be arbitrarily oriented, but their growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centered at the particles. The method is formulated for large deformations and arbitrary nonlinear and ratedependent materials; cohesive laws govern the traction-crack opening relations. To reduce computational cost and since more accuracy around the crack tip is needed to obtain adequate results, h-adaptivity is incorporated in the method. The model is applied to several three dimensional problems, some of which are compared to experimental data.

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“…The wider the crack opens, the smaller are the bond stresses. A more detailed description of the bond model is given in Rabczuk and Belytschko [35].…”

Section: Non-planar Crack Growthmentioning

confidence: 99%

A three-dimensional large deformation meshfree method for arbitrary evolving cracks

Rabczuk

Belytschko

2007

Computer Methods in Applied Mechanics and Engineering

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1,036

263

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“…While the bridging domain method was successfully applied in multiscale simulations -where often atoms were used instead of particles-as demonstrated by Xiao [51], the compatibility coupling e.g. was applied to static failure of reinforced concrete structures, [44]. Due to the wide application area, the limit of different numerical methods is not surprising.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Rabczuk and Belytschko [44] used this approach to couple EFG nodes and finite elements to model the bond behavior in reinforced concrete beams in statics. In this method, relative displacements between the particles and the elements are allowed.…”

Section: Compatibility Coupling:coupling With Lagrange Multipliersmentioning

confidence: 99%

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Coupling of mesh-free methods with finite elements: basic concepts and test results

Rabczuk

Xiao

Sauer

2006

Commun. Numer. Meth. Engng.

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183

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SUMMARYThis paper reviews several novel and older methods for coupling meshfree particle methods, particularly the elementfree Galerkin (EFG) method and the Smooth Particle Hydrodynamics (SPH), with finite elements. We study master slave couplings where particles are fixed across the finite element boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent from the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods.

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“…In that procedure moving least squares (MLS) shape functions are used in the EFG region of the problem domain, while hybrid shape functions, combining both MLS and FE shape functions, are used in the interface region. Other commonly used methods for FE-EFGM coupling are the continuous blending method in [14,15], methods based on Lagrange multipliers [16,17], on transition or bridge regions [18] and methods based on a collocation approach [19]. A comprehensive review of different FE-EFGM coupling procedures up to 2005 can be found in [20].…”

Section: Introductionmentioning

confidence: 99%

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

Ullah

Coombs

Augarde

2013

Computer Methods in Applied Mechanics and Engineering

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'An adaptive nite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems.', Computer methods in applied mechanics and engineering., 267 . pp. 111-132. Further information on publisher's website:http://dx.doi.org/10.1016/j.cma.2013.07.018Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 267, 2013, 10.1016/j.cma.2013.07.018. Additional 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-pro t 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. AbstractIn this paper, an automatic adaptive coupling procedure is proposed for the finite element method (FEM) and the element-free Galerkin method (EFGM) for linear elasticity and for problems with both material and geometrical nonlinearities. In this new procedure, initially the whole of the problem domain is modelled using the FEM. During an analysis, those finite elements which violate a predefined error measure are automatically converted to an EFG zone. This EFG zone can be further refined by adding nodes, thus avoiding computationally expensive FE remeshing. Local maximum entropy shape functions are used in the EFG zone of the problem domain for two reasons: their weak Kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the EFG and FE regions compared to the use of moving least squares basis functions. The Zienkiewicz & Zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the FE region of the problem domain, while the Chung & Belytschko error estimation procedure is used in the EFG region.

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Application of Particle Methods to Static Fracture of Reinforced Concrete Structures

Cited by 195 publications

References 41 publications

A three-dimensional large deformation meshfree method for arbitrary evolving cracks

A three-dimensional large deformation meshfree method for arbitrary evolving cracks

Coupling of mesh-free methods with finite elements: basic concepts and test results

An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

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