Element-free galerkin methods for static and dynamic fracture

SUMMARYA meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straight forward.

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“…Belytschko et al [16], Belytschko and Lu [17]. For the meshfree shell, at least a quadratic polynomial basis is required.…”

Section: Efg-meshfree Methodsmentioning

confidence: 99%

“…However, in meshfree methods, this technique cannot be applied analogously, see figure 3b, since there will always be particles with a partially cut domain of influence. Therefore, we introduce the branch function enrichment and use [17]:…”

Section: Methods 2: Local Partition Of Unity Approachmentioning

confidence: 99%

A meshfree thin shell method for non‐linear dynamic fracture

Rabczuk

Areias

Belytschko

2007

Numerical Meth Engineering

Self Cite

446

135

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“…As alreday mentioned, we consider the EFG-and SPH-method ( [7,8,9,16,41]) although the coupling ideas presented in this paper are in general applicable to most meshfree methods. A Lagrangian kernel is chosen, i.e.…”

Section: Meshfree Shape Functionsmentioning

confidence: 99%

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

Rabczuk

Xiao

Sauer

2006

Commun. Numer. Meth. Engng.

182

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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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“…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%

“…The obtained stress is then directly applied to the crack surfaces for the subsequent step of the calculation. In some respects, the basic model for traction-free cracks in the EFG method [18][19][20] is used for cohesive cracks without any modification. The cohesion effect on crack surfaces is in fact obtained by direct application of the transmitted tensile stress on the 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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Element-free galerkin methods for static and dynamic fracture

Cited by 380 publications

References 20 publications

A meshfree thin shell method for non‐linear dynamic fracture

A meshfree thin shell method for non‐linear dynamic fracture

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

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

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