Augmented element-free Galerkin framework for adaptive modelling of spatially graded orthotropic media under thermoelastic loads

In the present work, fracture analysis of orthotropic functionally graded materials subjected to thermoelastic loadings has been carried out using an extended element-free Galerkin method (EFGM). The formulation incorporates a rigorous mathematical modeling of orthotropic graded material properties and introduces an adaptive anisotropic moving least square approximation, wherein the nodal domain of influence evolves in size, shape and orientation based on spatial gradients of directional stiffness and thermal conductivity. This enables accurate interpolation in regions with steep material gradients, thereby overcoming the limitations of conventional isotropic support domains. Using this enhanced framework, various crack configurations including straight, inclined, multiple and kinked cracks in orthotropic-graded domains have been modeled for calculating mixed-mode stress intensity factors. Results revealed that mixed-mode stress intensity factors (SIFs) are strongly governed by the interaction between thermal gradients, material orthotropy and crack geometry, leading to progressive variations in both Mode I and Mode II stress intensity factors across diverse fracture configurations. Validation against multiple benchmark problems demonstrated excellent accuracy, with mean percentage deviation ranging between 1.05% and 2.35% across different test cases. Additional studies involving multiple-crack and kink-crack variations were also performed, further illustrating the robustness and modeling capability of the proposed framework under diverse thermo-mechanical conditions.