A non-local method in peridynamic theory for simulating elastic wave propagation in solids

Ma, Xinkai; Feng, Qingsong; Liu, Linya; Xu, Jiren; Zhang, Pengfei; Chen, Hua-Peng

doi:10.1016/j.apm.2021.10.041

Cited by 12 publications

(12 citation statements)

References 33 publications

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“…An increase (or decrease) in the angle 𝜙 k causes a rotation of the half-space around the point x i , as illustrated in Figure 4. For the construction of the ABCs, we adopt a symmetric interval in (34) to specify the angle 𝜙 k in order to transmit incoming waves from the near-field at different incident angles into their respective half-space. In addition, the value of Δ𝜙 must not be selected arbitrarily high, such that incident waves propagate out and the energy is absorbed.…”

Section: Semi-analytical Far-field Solutionmentioning

confidence: 99%

“…Another important note, alluded to in Section 3.1, is the selection of the parameters Δ𝜙 and Δ𝜅 as well as the associated ranges in (34). The application of EBFs is comprehensively studied in Reference 40, and possible ranges are provided in References 35-37.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…The application of EBFs is comprehensively studied in Reference 40, and possible ranges are provided in References 35-37. In the present study, following (34), an interval of Δ𝜙[−1, 1] with ten equidistant subdivisions is employed. Empirically, it has been found that a value of Δ𝜙 = 𝜋∕4 generally achieves satisfactory results.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…The influence of this parameter is presented by means of a sensitivity analysis in Reference 35. The second influential parameter Δ𝜅 in (34) affects the spatial fluctuation of the modes and determines the range of the interval Δ𝜅[−1, 1]. To find an upper limit to the value of Δ𝜅, we adopt the Nyquist-Shannon sampling theorem (see Reference 35).…”

Section: Numerical Implementationmentioning

confidence: 99%

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Dirichlet‐type absorbing boundary conditions for peridynamic scalar waves in two‐dimensional viscous media

Hermann

Shojaei

Seleson

et al. 2023

Numerical Meth Engineering

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Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave‐type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi‐analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane‐wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near‐field) with that of the exterior region (far‐field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two‐dimensional unbounded domains.

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Section: Semi-analytical Far-field Solutionmentioning

confidence: 99%

Section: Numerical Implementationmentioning

confidence: 99%

Section: Numerical Implementationmentioning

confidence: 99%

Section: Numerical Implementationmentioning

confidence: 99%

See 2 more Smart Citations

Dirichlet‐type absorbing boundary conditions for peridynamic scalar waves in two‐dimensional viscous media

Hermann

Shojaei

Seleson

et al. 2023

Numerical Meth Engineering

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“…In peridynamic theory, an integral model is used in place of the classic partial differential model, thus avoiding the invalidation problem, which usually appears under the classic mathematical framework due to discontinuity. After more than twenty years of development, peridynamic theory is now widely used in the study of elastic wave propagation [26], composite material fracture [27], rock failure [28] and corrosion damage [29], etc. Recently, with the advantages of dealing with fracture problems such as crack propagation, peridynamic theory has been preliminarily applied to the analysis of railway fatigue.…”

Section: Introductionmentioning

confidence: 99%

A two-dimensional ordinary state-based peridynamic model for surface fatigue crack propagation in railheads

Wang

et al. 2022

Engineering Fracture Mechanics

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Perfectly matched layers for peridynamic scalar waves and the numerical discretization on real coordinate space

Du,

Zhang

2023

Numerical Meth Engineering

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Nonlocal perfectly matched layers (nonlocal PMLs) for nonlocal wave equations and the corresponding numerical discretization to solve the reduced PML problems on bounded domains are studied. The nonlocal PMLs are derived by combining the Laplace transform and the analytical continuation into the complex plane. The discrete scheme defined on the complex space may lead to a spurious imaginary part of the numerical solution and has a large computational cost. Here we design some new nonlocal PMLs and numerical schemes and prove that they are on the real space, which is much efficient comparing with the complex space. The accuracy and effectiveness of our approaches are illustrated by some numerical examples.

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A non-local method in peridynamic theory for simulating elastic wave propagation in solids

Cited by 12 publications

References 33 publications

Dirichlet‐type absorbing boundary conditions for peridynamic scalar waves in two‐dimensional viscous media

Dirichlet‐type absorbing boundary conditions for peridynamic scalar waves in two‐dimensional viscous media

A two-dimensional ordinary state-based peridynamic model for surface fatigue crack propagation in railheads

Perfectly matched layers for peridynamic scalar waves and the numerical discretization on real coordinate space

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