Peridynamic modeling of Lamb wave propagation in bimaterial plates

Alebrahim, Reza

doi:10.1016/j.compstruct.2019.01.108

Cited by 22 publications

(8 citation statements)

References 33 publications

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“…It is a highly accurate method for flows with periodic boundary conditions, and is suitable for nonlinear problems, especially because moves the convolution products into multiplications in the spectral space. In particular, it is widely implemented in linear peridynamic problems where the computation of a convolution integral is required (see, for instance, References 17,23,[29][30][31].…”

Section: Spatial Spectral Semidiscretizationmentioning

confidence: 99%

A spectral method with volume penalization for a nonlinear peridynamic model

Lopez

Pellegrino

2020

Numerical Meth Engineering

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The peridynamic equation consists in an integro‐differential equation of the second order in time which has been proposed for modeling fractures and damages in the context of nonlocal continuum mechanics. In this article, we study numerical methods for the one‐dimension nonlinear peridynamic problems. In particular we consider spectral Fourier techniques for the spatial domain while we will use the Störmer–Verlet method for the time discretization. In order to overcome the limitation of working on periodic domains due to the spectral techniques we will employ a volume penalization method. The performance of our approach is validated with the study of the convergence with respect to the spatial discretization and the volume penalization. Several tests have been performed to investigate the properties of the solutions.

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Section: Spatial Spectral Semidiscretizationmentioning

confidence: 99%

A spectral method with volume penalization for a nonlinear peridynamic model

Lopez

Pellegrino

2020

Numerical Meth Engineering

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“…The set of unknown coefficients is obtained by projecting the residual, Eqs. (31) or (36), on the basis functionsk [see Eq. (30)] or {Ā i } [see Eq.…”

Section: Galerkin Methodsmentioning

confidence: 99%

“…They have concluded that their proposed method can mitigate wave dispersion and it is able to reduce the oscillation of the stress intensity factor at the crack tip. Modeling of Lamb wave propagation in bimaterial plates was proposed by Alebrahim [31] who concluded that although PD produces accurate solution for the evaluation of symmetric Lamb waves, it is not able to model antisymmetric Lamb waves accurately.…”

Section: Introductionmentioning

confidence: 99%

Improved wave dispersion properties in 1D and 2D bond-based peridynamic media

et al. 2021

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In this study, a novel method for improving the simulation of wave propagation in Peridynamic (PD) media is investigated. Initially, the dispersion properties of the nonlocal Bond-Based Peridynamic model are computed for 1-D and 2-D uniform grids. The optimization problem, developed through inverse analysis, is set up by comparing exact and numerical dispersion and minimizing the error. Various weighted residual techniques, i.e., point collocation, sub-domain collocation, least square approximation and the Galerkin method, are adopted and the modification of the wave dispersion is then proposed. It is found that the proposed methods are able to significantly improve the description of wave dispersion phenomena in both 1-D and 2-D PD models.

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“…25,26,28 Oftentimes, the parameters are weighted with the fraction of the bond length associated with the respective material. These approaches can further be classified into arithmetic averaging 6,[35][36][37] and harmonic averaging. 6,7,9,38 Cheng et al 26 used the proportion of the material coefficients to identify a weighting factor.…”

Section: Introductionmentioning

confidence: 99%

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

Laurien

Javili

Steinmann

2022

Numerical Meth Engineering

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In this contribution, we present a novel approach on how to treat material interfaces in nonlocal models based on peridynamics (PD) and in particular continuum-kinematics-inspired peridynamics (CPD), a novel variationally consistent peridynamic formulation. Our method relies on a nonlocal interface where the material subdomains overlap. Within this region, a kinematic coupling of the two constituents is enforced. The contact is purely geometrical as interaction forces act only between points of the same material. We provide a detailed description of the computational implementation within the framework of CPD, that is in principle applicable to all formulations of PD. A variety of numerical examples for modeling bimaterial interfaces illustrate the utility of the technique for both two-dimensional and three-dimensional problems, including examples at large deformations. Our model approaches a local model when the nonlocality parameter, the horizon size, is decreased. The proposed methodology offers a viable alternative to previous approaches in PD, which are essentially imposing mixture rules for the interfacial material parameters.

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Peridynamic modeling of Lamb wave propagation in bimaterial plates

Cited by 22 publications

References 33 publications

A spectral method with volume penalization for a nonlinear peridynamic model

A spectral method with volume penalization for a nonlinear peridynamic model

Improved wave dispersion properties in 1D and 2D bond-based peridynamic media

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

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