A Re-Examination of Wave Dispersion and on Equivalent Spatial Gradient of the Integral in Bond-Based Peridynamics

Mutnuri, VS and Gopalakrishnan, S (2020) A Re-Examination of Wave Dispersion and on Equivalent Spatial Gradient of the Integral in Bond-Based Peridynamics. In: Journal of Peridynamics and Nonlocal Modeling . ISSN 2522-896X

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Abstract

In this paper, wave dispersion properties in bond-based peridynamics (BBPD) are reexamined. By BBPD formulation, wave dispersion (frequency (ω) - wavenumber (k)) relation is known to be transcendental in nature. In fact, for uniform micromodulus function (C), there exists a frequency bandwidth with multiple k. Further, there is a ω within this bandwidth at which propagating k are infinite in number. Question that needs an answer is canallk propagate in the BBPD? In literature, an agreement between certain continuum gradient models (CM) and BBPD has been reported. This agreement is established in the sense that, for a judicious choice of C, wave dispersion properties are the same between BBPD and CM. This equivalence between a finite-ordered (CM) and an infinite-ordered (BBPD) displacement gradient model motivates to an associated converse question: given a C, does BBPD integral represent an effective displacement gradient of a finite order? In this paper, an attempt has been made to fix an order to the BBPD integral with the help of a Fourier frequency-based spectral study, under a one-dimensional rod setting. Both kinetically local and nonlocal formulations of BBPD are considered. It is argued that only one wave mode may propagate in a BBPD rod.This implies, Neumann force condition at a boundary should read as a spatial gradient of order one. This further implies, the BBPD spatial integral effectively represents a second-order displacement gradient in space. The wave motion study of this papercorroborateswith the literature that applies localboundaryconditions to nonlocal boundary value problems.

Item Type:	Journal Article
Publication:	Journal of Peridynamics and Nonlocal Modeling
Additional Information:	copyright for this article belongs to Springer
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	04 Jun 2020 05:37
Last Modified:	06 Jun 2020 17:43
URI:	http://eprints.iisc.ac.in/id/eprint/65272

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