The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

Krysl, Petr; Belytschko, Ted

doi:10.1002/(sici)1097-0207(19990228)44:6<767::aid-nme524>3.0.co;2-g

Cited by 238 publications

(82 citation statements)

References 56 publications

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“…The integrals in (25) and (27) are evaluated by stress point integration similar to Rabczuk and Belytschko [36]. The particle masses and volumes are obtained via a Voronoi tesselation.…”

Section: Integration and Particle Masses And Volumesmentioning

confidence: 99%

“…Previous meshfree methods for the modelling of cracks (Belytschko and Tabbara [11], Lu et al [29], Belytschko and Lu [8], Belytschko et al [9] and Krysl and Belytschko [25]) also used explicit representations of the crack. In the three-dimensional method in [25], surface models were constructed from 3-node triangular facets.…”

Section: Introductionmentioning

confidence: 99%

“…In the three-dimensional method in [25], surface models were constructed from 3-node triangular facets.…”

Section: Introductionmentioning

confidence: 99%

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

Rabczuk

Belytschko

2007

Computer Methods in Applied Mechanics and Engineering

998

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 integrals in (25) and (27) are evaluated by stress point integration similar to Rabczuk and Belytschko [36]. The particle masses and volumes are obtained via a Voronoi tesselation.…”

Section: Integration and Particle Masses And Volumesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Rabczuk

Belytschko

2007

Computer Methods in Applied Mechanics and Engineering

998

263

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“…The concept of extending surfaces within the domain to represent crack propagation is actually similar to the treatment of cracks in the boundary element method [12][13][14][15][16]. Several extensions of the EFG method to model crack propagation have been proposed [17][18][19][20][21][22][23][24][25][26][27][28]. However, all of these works are related to brittle cracks with no traction force between crack surfaces.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Cohesive Crack Growth by the Element-Free Galerkin Method

Soparat

Nanakorn

2008

J. mech.

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In this study, the element-free Galerkin (EFG) method is extended to include nonlinear behavior of cohesive cracks in 2D domains. A cohesive curved crack is modeled by using several straight-line interface elements connected to form the crack. The constitutive law of cohesive cracks is considered through the use of these interface elements. The stiffness equation of the domain is constructed by directly including, in the weak form of the global system equation, a term related to the energy dissipation along the interface elements. The constitutive law of cohesive cracks can then be considered directly and efficiently by using this energy term. The validity and efficiency of the proposed method are discussed by using problems found in the literature. The proposed method is found to be an efficient method for simulating propagation of cohesive cracks.

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“…Fracture simulation work in two and three dimensions using meshfree methods is extensive [19,20,21,22,23], in which discontinuities are treated by the visibility criterion or some modifications of it. Other novel approaches which were able to treat kinked and curved cracks were proposed by Ventura et al [24].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment

Bordas

Zi²,

Rabczuk

2007

IUTAM Symposium on Discretization Methods for Evolving Discontinuities

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This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, branching, growth and coalescence of an arbitrary number of cracks in non-linear solids including large deformations, for statics and dynamics. The novelty of the methodology is that only an extrinsic discontinuous enrichment and no near-tip enrichment is required. Instead, a Lagrange multiplier field is added along the crack front to close the crack. This decreases the computational cost and removes difficulties involved with a branch enrichment. The results are compared to experimental data, and other simulations from the literature to show the robustness and accuracy of the method.

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The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

Cited by 238 publications

References 56 publications

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

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

Analysis of Cohesive Crack Growth by the Element-Free Galerkin Method

Three-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment

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