Paper Title
Crack Propagation Using in Direct Boundary Element Methods

Abstract
In this study, the purpose of obtaining the influence functions of the displacement discontinuity in anisotropicelastic medium is to produce the boundary element equations. AD is placement Discontinuous Method formulation (DDM) is presented with the aim of modeling two-dimension alelastic fracture problems. This formulation is found by analytical integration of the fundamental solution along a straight -line crack. With this purpose, Kelvin fundamental solutions for isotropic media on infinite plane isused to for mdipoles from singular loads, and the various combinations of the said dipoles are used to obtain the influence functions of the displacement discontinuity. This study introduces a technique in coupling the Fictitious Stress Method (FSM) and Domain Decomposition Method (DDM). The reason for applying this technique to some examples is to demonstrate the effectiveness of the proposed coupling method. In these applications, Mode I and Mode II stress intensity factors at the crack tips, as well as stresses and displacements at the cracks, were calculated, and the results were compared with tables. A comparison is made between two indirect boundary element formulations: DDM and an extension of FSM for solving problems involving cracks. Crack propagation was investigated using these methods. Several numerical examples are presented, and the Stress Intensity Factor (SIF) outcomes are contrasted with existing analytical or reference results.