Fast Solution of Initial Value Problems for Wave Propagation in Peridynamic Media

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 verified using a spherical Bessel function series solution. A nonlinear dispersion relation is derived using Floquet theory for a periodic elastic medium of infinite extent, which we use to solve an IVP for a homogenized peridynamic medium using our IFFT algorithm; this solution compares well with a spherical Bessel function series solution. 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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2022
Accession Number
AD1179213

Entities

People

  • Burak Aksoylu
  • George A. Gazonas
  • Raymond A. Wildman

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Band Structures
  • Bessel Functions
  • Composite Materials
  • Computational Science
  • Computer Programs
  • Differential Equations
  • Dispersion Relations
  • Elastic Properties
  • Equations
  • Fast Fourier Transforms
  • Frequency
  • Group Velocity
  • Integrals
  • Linear Momentum
  • Mechanics
  • Modulus Of Elasticity
  • Wave Equations
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Wave Propagation and Nonlinear Chaotic Dynamics.