Subdomain radial basis collocation method for fracture mechanics

The direct approximation of strong form using radial basis functions (RBFs), commonly called the radial basis collocation method (RBCM), has been recognized as an effective means for solving boundary value problems. Nevertheless, the non-compactness of the RBFs precludes its application to problems with local features, such as fracture problems, among others. This work attempts to apply RBCM to fracture mechanics by introducing a domain decomposition technique with proper interface conditions. The proposed method allows (1) natural representation of discontinuity across the crack surfaces and (2) enrichment of crack-tip solution in a local subdomain. With the proper domain decomposition and interface conditions, exponential convergence rate can be achieved while keeping the discrete system well-conditioned. The analytical prediction and numerical results demonstrate that an optimal dimension of the near-tip subdomain exists. The effectiveness of the proposed method is justified by the mathematical analysis and demonstrated by the numerical examples.