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.
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