A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks

Rabczuk, Timon; Zi, Goangseup

doi:10.1007/s00466-006-0067-4

Cited by 280 publications

(101 citation statements)

References 43 publications

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“…The concept of local partition of unity and level sets were incorporated in a meshfree context for linear elastic cracks by Ventura [26] and for cohesive cracks by Rabczuk and Zi [27].…”

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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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“…The concept of local partition of unity and level sets were incorporated in a meshfree context for linear elastic cracks by Ventura [26] and for cohesive cracks by Rabczuk and Zi [27].…”

mentioning

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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“…Since analytical solutions provide limited information, there has been a keen interest in numerically simulating fracture in thin shells in recent years. However, despite the advances made in modeling fracture for solid bodies [1,2,3,4,5], fracture in thin bodies remains a challenge due to the complex interplay between cracks and the shell kinematics and geometry.…”

Section: Introductionmentioning

confidence: 99%

Phase-field modeling of fracture in linear thin shells

Amiri

Millán

Shen

et al. 2014

Theoretical and Applied Fracture Mechanics

285

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We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximumentropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.

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“…Meshless methods remain of interest in the computational mechanics community, in particular the element-free Galerkin method (EFGM) [1], because in these methods only a set of nodes is required for the problem discretisation, making them ideal for modelling problems with large deformation, material damage, projectile penetration, fragmentation, crack growth and moving boundaries, the details of which can be found in [2,3,4,5,6,7,8,9,10,11,12]. However it is well-known that they tend to be more computationally expensive than finite element methods (FEMs) set the same job.…”

Section: Introductionmentioning

confidence: 99%

“…The corresponding refinement strategy is then given in §5.2 and the full adaptively coupled FE-EFGM algorithm is described in §5. 3. Numerical examples are given in §6 to show the implementation and performance of the proposed adaptive FE-EFGM method.…”

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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A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks

Cited by 280 publications

References 43 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

Phase-field modeling of fracture in linear thin shells

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

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