Applicability and Relative Performance of some Mesh-Reduction Methods for Fracture Analysis of Mode III Cracks

Popularity in the application of mesh-reduction methods for the solution of many physical/engineering problems governed by some PDEs is on increase by the day. This happens du...ue to their simplicity and several other advantages over the fully mesh-based methods such as the finite element method (FEM). The meshless methods possess high potentials and satisfactory performance for crack analysis in the field of fracture mechanics due to the fact that they require no re-meshing when applied to solve such problems. The analytical methods for elastic crack problems are mostly adopted to provide solutions which are singular and localized (valid only around the crack tip field). Due to the numerous advantages of the mesh-reduction methods over the fully mesh-based techniques, the present study will investigate the applicability and relative performance of the boundary element method (BEM), the method of fundamental solutions (MFS) and the radial basis function (RBF) in augmenting the localized analytical solution in order to come up with a robust solution that captures the singular stresses at the crack tip while satisfying the boundary conditions. Having applied these techniques by some researchers to solve crack problems in solids, the new thing in the proposed work is that it is aimed at providing an insight into the relative accuracy and flexibility of the mentioned techniques in the fracture analysis of mode III cracks. The solutions will be obtained by eliminating the need for meshing contrary to that needed in some other traditional and long-established methods. Consequently, reduction in time and computational efforts will be incurred. Both direct and enriched version of the BEM, MFS and RBF for mode III crack problems will be studied. In addition, either the single-domain or the domain decomposition approach will be utilized to arrive at the solutions. In addition to satisfying its main objectives, this research project will also serve the purpose of providing the performance of the benchmarked methods and methodology that will later be utilized for future studies of mode I and mode II crack analyses.