Peridynamic Modeling of Diffusion by Using Finite-Element Analysis

Abstract

Diffusion modeling is essential in understanding many physical phenomena such as heat transfer, moisture concentration, and electrical conductivity. In the presence of material and geometric discontinuities and nonlocal effects, a nonlocal continuum approach, named peridynamics (PD), can be advantageous over the traditional local approaches. PD is based on integro-differential equations without including any spatial derivatives. In general, these equations are solved numerically by employing meshless discretization techniques. Although fundamentally different, commercial finite-element software can be a suitable platform for PD simulations that may result in several computational benefits. Hence, this paper presents the PD diffusion modeling and implementation procedure in a widely used commercial finite-element analysis software, ANSYS. The accuracy and capability of this approach is demonstrated by considering several benchmark problems.