New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics

Abstract

Recent analytical solutions for peridynamic (PD) models of transient diffusion and elastodynamics allow us to revisit convergence of 1D PD models to their classical counterparts. We find and explain the reasons for some interesting differences between the convergence behavior for transient diffusion and elastodynamics models. Except for very early times, PD models for transient diffusion converge monotonically to the classical one. In contrast, for elastodynamic problems this convergence is more complex, with some periodic/almost-periodic characteristics present. These special features are investigated for sine waves used as initial conditions. The analysis indicates that the convergence behavior of PD solutions to the classical one can be understood in terms of convergence properties for models using the Fourier series expansion terms of a particular initial condition. The results obtained show new connections between PD models and their corresponding classical versions.