Numerical Green's Functions for Line Force and Dislocation around Multiple Cracks

Abstract

The numerical Green's function technique for an infinite isotropic domain with multiple cracks is developed. The singularities considered are the line force and dislocation. The Green's function is decomposed into the singular and the image terms. To obtain the image term we represent the crack opening displacement (COD) by the dislocation dipole distribution, embed the √r crack tip behavior, and integrate the resulting singular/hyper-singular integrals analytically. The resulting whole crack singular element (WCSE) consists of multiple independent crack opening modes and is strictly algebraic with the correct crack tip singular behavior but the magnitude for each mode is unknown. They are determined to give the negative of the crack surface traction induced by the singular term. Extensive error analysis is performed for the line force and dislocation in an infinite domain with a single crack to identify the region where, when these singularities are placed, the solution achieves high accuracy. Following the guideline set by the error analysis, numerical Green's functions for a few multiple crack configurations are obtained for the line force and dislocation.