A Coarsening Method for Linear Peridynamics

Silling, Stewart A.

doi:10.1615/intjmultcompeng.2011002674

Cited by 33 publications

(4 citation statements)

References 13 publications

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“…According to the assumption in PD theory, the SLGS is composed of infinitesimally small material points and each material point consists of a cluster of atoms, for which the current model is called the OSPD-CG model. In an early study, Silling [47] proposed a linear BPD-CG method, which could accurately reproduce the effective elastic properties of a composite as well as the effect of a small defect in a homogeneous medium. Based on a linear material model, Oterkus et al [35] simulated the fracture of SLGS using peridynamics and captured the crack branching behaviour in SLGS, but the final fracture pattern was different from the fully atomistic MD simulation results due to the nonlinear material property of SLGS.…”

Section: Ordinary State-based Peridynamic Coarse-graining Model Of Single-layer Graphene Sheetsmentioning

confidence: 99%

An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets

Liu

Wang

et al. 2018

Proc. R. Soc. A.

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This study develops an ordinary state-based peridynamic coarse-graining (OSPD-CG) model for the investigation of fracture in single-layer graphene sheets (SLGS), in which the peridynamic (PD) parameters are derived through combining the PD model and molecular dynamics (MD) simulations from the fully atomistic system via energy conservation. The fracture failure of pre-cracked SLGS under uniaxial tension is studied using the proposed PD model. And the PD simulation results agree well with those from MD simulations, including the stress–strain relations, the crack propagation patterns and the average crack propagation velocities. The interaction effect between cracks located at the centre and the edge on the crack propagation of the pre-cracked SLGS is discussed in detail. This work shows that the proposed PD model is much more efficient than the MD simulations and, thus, indicates that the PD-based method is applicable to study larger nanoscale systems.

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Section: Ordinary State-based Peridynamic Coarse-graining Model Of Single-layer Graphene Sheetsmentioning

confidence: 99%

An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets

Liu

Wang

et al. 2018

Proc. R. Soc. A.

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“…S.A. Silling [11,12] proposed a non-local peridynamic (PD) theory that doesn't rely on spatial derivatives, unlike previous non-local theories. The non-local PD theory provides nonlinear material response and includes damage [13][14][15][16]. K. Naumenko and V.A.…”

Section: Introductionmentioning

confidence: 99%

Experimental and Numerical Investigation of Intact and Cracked Steel Plates under tensile loading using Non-local Method

Abadi,

Kabir

2024

Preprint

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This study examines intact and cracked steel plates under uniform tensile loading, using local and non-local methods, and predicts crack growth with the energy released rate criterion. The impact of initial crack orientation, crack development, crack branching, the number of material points, and the horizon size on the ultimate strength of the steel plates are analyzed. Non-local relationships are established and applied to the equation of motion, with the principle of virtual work employed to solve the associated Lagrange equation. The study determines that the accuracy of the model improves with a horizon function length closer to 0.4 mm, and increasing the number of material points from 50 to 250 enables a more accurate evaluation of crack branching. The lowest and highest load capacities are related to plates with double and single-edge cracks, respectively. The study also shows that as the crack angle increases, the plate's load-carrying capacity under tensile loading increases. The effect of loading speed rate on the intensification of crack branching is investigated, and the results of the non-local method are compared with numerical approaches and experimental tests, showing a maximum difference of 2.13%. The robustness of the developed non-local method for predicting crack growth path, micro-cracks, and branching of cracks is demonstrated thoroughly in comparison with other numerical approaches and experimental tests. In summary, our study offers insights into steel plate behavior under tensile loads and introduces a new approach to predict crack growth, improving safety and reliability in critical steel structures.

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“…PD has also been employed to study other nonlocal physical processes such as metal machining process [20], diffusion and other transport phenomena [21][22][23]. Peridynamic frameworks have also been proposed for homogenisation of heterogeneous materials [24][25][26][27][28][29][30][31] as well as multiscale [32][33][34][35][36][37][38] and Multiphysics modelling [39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

Galadima

Oterkus

Öterkuş

et al. 2023

Engineering with Computers

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This paper proposes a framework for implementing viscoelastic constitutive model from the classical continuum mechanics (CCM) theory within non-ordinary state-based peridynamics (NOSBPD). The motivation stems from the inadequacy of CCM to model very complex material behaviours such as initiation and propagation of cracks and nonlocal behaviour due to size effects. The proposed formulation leverages on the constitutive correspondence between NOSBPD and CCM to incorporate a CCM viscoelastic constitutive model based on hereditary integral into NOSBPD. The combination of hereditary constitutive model and NOSBPD effectively makes this formulation a nonlocal time–space viscoelastic framework where temporal nonlocality is incorporated by a hereditary viscoelastic model which stipulates that the behaviour of a material at any point in time depends on both the present action and the complete history of previous actions on the material, and spatial nonlocality on the other hand is incorporated via the nonlocal mechanism provided by the NOSBPD. For model validation, three benchmark problems were solved using the proposed framework. Results obtained were compared to results from analytical solution and solutions from referenced literature. In addition, parametric study was conducted to determine the influence of nonlocality on numerical prediction. Conclusions drawn from the validation studies presented are that the proposed framework is able to predict viscoelastic responses that agree well with local macro models as well as nonlocal micromodels/nanomodels as reported in the literature.

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A Coarsening Method for Linear Peridynamics

Cited by 33 publications

References 13 publications

An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets

An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets

Experimental and Numerical Investigation of Intact and Cracked Steel Plates under tensile loading using Non-local Method

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

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