A coupling approach of discretized peridynamics with finite element method

Liu, Wenyang; Hong, Jung‐Wuk

doi:10.1016/j.cma.2012.07.006

Cited by 169 publications

(94 citation statements)

References 63 publications

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“…The CT-coupling scheme given by Liu and Hong (2012a), which distributes a coupling force among FE nodes of the plane segment at the interface with the PD-subregion, is realized by the code. Therefore, 2D-shape functions, implemented in the routine shapefunctions2D, must be used.…”

Section: Sequential Peridynamics Code Coupled With Finite Element Methodsmentioning

confidence: 99%

“…Ha and Bobaru (2011) also found that the peridynamics code presents crack branching and its secondary crack. Liu and Hong (2012a) observed two curvilinear crack paths under the interaction effect between approaching crack propagations. Ha et al (2015) studied the cracking mechanism of tensile wing cracks and secondary cracks of a single inborn flaw.…”

Section: Introductionmentioning

confidence: 92%

“…For the approach coupling peridynamics and an FEM, an interface element is introduced by Liu and Hong (2012a). To calculate coupling forces, a number of peridynamic (PD)-nodes are embedded in the interface element and these interact with PD-nodes in the peridynamic region (Fig.…”

Section: Brief Review Of Peridynamic Formulation Coupled With Finite mentioning

confidence: 99%

“…The coupling forces, f cp , on embedded nodes are divided among the finite element (FE)-nodes on the interface segment as (Liu and Hong 2012a) …”

Section: Brief Review Of Peridynamic Formulation Coupled With Finite mentioning

confidence: 99%

“…Several researchers have addressed these problems using a variety of techniques. Liu and Hong (2012a) proposed a coupling approach for peridynamics and finite element methods (FEM). The scheme focuses on a region in which a crack is more likely to occur, and this region is modeled by peridynamics, which calculates the discontinuities.…”

Section: Introductionmentioning

confidence: 99%

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Parallel programming of a peridynamics code coupled with finite element method

Lee

Hong

2016

Int J Fract

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Using OpenMP (the Open MultiProcessing application programming interface), dynamic peridynamics code coupled with a finite element method is parallelized. The parallel implementation improves run-time efficiency and makes the realistic simulation of crack coalescence possible. To assess the accuracy and efficiency of the parallel code, we investigate its speedup and scalability. In addition, to validate the parallel code, experimental results for crack coalescence development sequences are compared. It is noted that this parallelized code markedly reduces computation time along with the coupling scheme. Moreover, the coupling approach used in this parallel code enables a more realistic and feasible numerical prediction of coalescing fractures. With the parallel implementation, two main types of crack coalescences between two flaws, formed by two short shear cracks and by a short central tensile segment and subsequent shear cracks are in detail discussed in terms of their development sequences. Consequently, this proposed coupled peridynamics code can be used to efficiently solve actual coalescence development sequences, thereby providing a numerical solution for fracture mechanics.

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Section: Sequential Peridynamics Code Coupled With Finite Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

Section: Brief Review Of Peridynamic Formulation Coupled With Finite mentioning

confidence: 99%

“…The coupling forces, f cp , on embedded nodes are divided among the finite element (FE)-nodes on the interface segment as (Liu and Hong 2012a) …”

Section: Brief Review Of Peridynamic Formulation Coupled With Finite mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parallel programming of a peridynamics code coupled with finite element method

Lee

Hong

2016

Int J Fract

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Morphological aspects of crack growth in rock materials with various flaws

Lee

Hong

2019

Num Anal Meth Geomechanics

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Summary Crack evolution is initiated by the occurrence of tensile wing cracks and is then further promoted due to the crack coalescence caused by the extension of a central tensile crack segment between two relatively adjacent flaws. To understand such progressive failures in rock, a parallelized peridynamics coupled with a finite element method is utilized. Through this method, the initiation position of tensile wing cracks is observed with respect to varying inclination angles of a flaw, and then its corresponding shifting mechanism is investigated. In addition, the phenomenon of the position shifting being sensitive to various flaw shapes is discussed. Moreover, it is observed that the inclination angle of a central flaw affects the initiation position of other flaws; therefore, the initiation positions of tensile wing crack emanating from other neighboring flaws are analyzed with their angles. Following tensile wing cracks, a central tensile crack segment occurs in the bridging region between a central flaw and other neighboring flaws; the developmental patterns caused by the crack segment are discussed as well. Finally, the role a central tensile crack segment plays in the formation of crack coalescence and specimen failure is investigated in detail. The numerical results in this paper demonstrate good fidelity with established physical test results and complement them, thereby expanding the understanding of fracturing morphology in rock specimens with various flaws.

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Voronoi‐based peridynamics and cracking analysis with adaptive refinement

Zhang

Xia

2017

Numerical Meth Engineering

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The most common technique for the numerical implementation of peridynamic theory is the uniform discretization together with constant horizon. However, unlike the nonuniform discretization and varying horizons, it is not a natural and intrinsic component of the adaptive refinement analysis and multiscale modeling. Besides, it encounters discretization difficulty in analyzing irregular structures. Therefore, to analyze problems with nonuniform discretization and varying horizons and solve the resulting problems of ghost forces and spurious wave reflection, the dual-horizon peridynamics based on uniform discretization is extended to the nonuniform discretization based on Voronoi diagrams, for which we call it Voronoi-based peridynamics. We redefine the damage definition as well. Next, an adaptive refinement analysis method based on the proposed Voronoi-based peridynamics and its numerical implementation is introduced. Finally, the traditional bond-based peridynamics and the Voronoi-based peridynamics with or without refinement are used to simulate 4 benchmark problems. The examples of 2-D quasi-static elastic deformation, 2-D wave propagation, 2-D dynamic crack growth, and 3-D simulation of the Kalthoff-Winkler experiment demonstrate the efficiency and effectivity of the proposed Voronoi-based peridynamics. Further, the adaptive refinement analysis can be used to obtain reasonable crack path and crack propagation speed with reduced computational burden.

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A coupling approach of discretized peridynamics with finite element method

Cited by 169 publications

References 63 publications

Parallel programming of a peridynamics code coupled with finite element method

Parallel programming of a peridynamics code coupled with finite element method

Morphological aspects of crack growth in rock materials with various flaws

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

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