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Fast Fourier transform-based solutions of initial value problems for wave propagation in microelastic media

George A. Gazonas, Burak Aksoylu and Raymond A. Wildman

Vol. 19 (2024), No. 1, 61–89
DOI: 10.2140/jomms.2024.19.61
Abstract

An inverse fast Fourier transform (IFFT) algorithm is developed to solve initial value problems (IVPs) for wave propagation in nonlocal peridynamic media. The IFFT solutions compare well with solutions obtained using Mathematica’s NIntegrate function and are verified using a spherical Bessel function series solution. We solve a peridynamic microelastic IVP by using Floquet theory to determine a nonlinear dispersion relation for a periodically layered elastic medium and demonstrate that microelastic peridynamic IVP solutions can be used to represent the behavior of homogenized waves in periodic elastic media. A local-nonlocal peridynamic correspondence principle is identified, which enables direct determination of nonlocal Fourier transform domain solutions to IVPs; the correspondence principle only requires identification of the nonlinear dispersion curve for the material and does not require definition of a micromodulus function, although the latter is implicitly defined via an integral equation. Results are useful for modeling and verification of dispersive wave propagation in large-scale peridynamic numerical simulations.

Keywords
inverse fast Fourier transform, initial value problem, peridynamics, correspondence principle, dispersion, nonlocal, Mathematica source code
Milestones
Received: 7 June 2023
Revised: 19 October 2023
Accepted: 20 November 2023
Published: 22 December 2023
Authors
George A. Gazonas
Army Research Directorate
DEVCOM Army Research Laboratory
Aberdeen Proving Ground, MD
United States
Burak Aksoylu
Department of Mathematical, Physical and Engineering Sciences
Texas A&M University-San Antonio
San Antonio, TX
United States
Raymond A. Wildman
Sandia National Laboratories
Albuquerque, NM
United States