An Analysis of Wave Dispersion in an Anisotropic Medium Through Peridynamic Theory

Peridynamic (PD) theory is a mathematical framework that utilizes integro-differential equations instead of the conventional partial differential equations employed in classical continuum mechanics. The peridynamic modeling of elastic wave propagation in three-dimensional anisotropic materials remains in its initial stages, as anisotropic material properties change with direction. In this study, an analysis of the plane wave is performed to determine the dispersion relation for plane waves in three-dimensional anisotropic media. The general solution for the initial-value problem is presented, and the closed-form expression for displacement in terms of Green’s function is derived for the first time for anisotropic materials. This paper focuses on several nonlocality functions, including Gaussian, linear, and constant functions. Graphs are demonstrated to illustrate the variations in frequency, phase velocity, and group velocity with changes in the size of the horizon (which represents nonlocal length) and nonlocality functions. Subsequently, the significant findings are analyzed and discussed. A thorough comprehension of peri-elastodynamics is essential for effective simulation and analysis to leverage its potential for nondestructive evaluation (NDE) and structural health monitoring.