Anisotropic hygrothermal fracture mechanics in orthotropic materials: A novel efficient interpolating modified MLS-based EFGM employing radial basis function

Abstract

A novel Wendland’s radial basis function (RBF) based Interpolating Modified MLS-based (IMMLS) technique in EFGM is proposed and demonstrated in this work. Anisotropic Hygrothermoelastic Fracture Mechanics (AHFM) problems with orthotropic material model are employed to illustrate Wendland’s RBF-based IMMLS technique and, in addition, to address the research gap in EFGM formulations for these problems. The Wendland’s RBF-based IMMLS EFGM, like IMMLS EFGM incorporating regularized weight functions (RWF), results in interpolating shape functions which address the limitations of classical MLSA-based EFGM. To assess efficacy, an illustrative case is benchmarked with FEM. For all the EFG techniques — formulated using Wendland’s RBF, RWFs, and classical MLSA-based EFGM, L2 norm results show a good correspondence with FEM. Subsequently, a comparative study among various EFG techniques is undertaken for Mode 1 and Mixed-mode cases incorporating regular and irregular nodal configurations. In comparison to the classical MLSA-based EFGM, IMMLS results employing Wendland’s RBF and RWFs corroborate closely with FEM results and show better computational efficiency. On the other hand, Wendland’s RBF-based IMMLS yields results similar to RWF-based IMMLS with nearly similar computational efficiency and advantages. Thus, Wendland’s RBF-based IMMLS extends the class of IMMLS techniques and offers a potential tool to solve fracture mechanics problems.