Abstract
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.
Highlights
The topic of the present work is the study of wave propagation in solid media described with a Peridynamic model
The Galerkin method is applied to find the unknown scaling coefficients α corresponding to the optimized 1-D and 2-D non-local Peridynamic models
I.e., point collocation, sub-domain collocation, least square approximation and the Galerkin method, were proposed and scaling coefficients corresponding to all bonds were computed
Summary
The topic of the present work is the study of wave propagation in solid media described with a Peridynamic model. In another study Wildman and Gazonas [30] improved the wave dispersion behavior in Peridynamic through combining with a finite difference method. 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. It was found that the numerical dispersion can be substantially improved by a proper choice of the influence function, in particular if it coincides with the kernel function of the nonlocal solid proposed in [32] Such an approach was presented in [33] for computing weight coefficients correcting the numerical dispersion error.
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