An efficient meshfree framework for simulation of crack tip stress fields in two-dimensional graded media subjected to thermoelastic loads

Abstract In the present work a novel framework of algorithm has been proposed for enhancing the versatility of the element-free Galerkin method for modeling of fracture in graded media subjected to thermoelastic loadings. The proposed work restructures the conventional element free Galerkin method (EFGM) at multiple level through generic MATLAB algorithms thereby developing an efficient and robust method for simulating crack tip stress fields in graded material subjected to thermoelastic loads. The proposed algorithm utilizes varying nodal density criterion in conjunction with optimum Gaussian quadrature around these nodes for numerical integration of the governing equations. The proposed algorithm also incorporates blended approximation which is effective for simulating crack tip stress fields in both convex and non-convex problem domains. Nonequilibrium formulation has been selected for evaluating stress intensity factors (SIFs) for the fracture problems in graded media. A few problems of cracked domain subjected to thermoelastic loads have been modeled and simulated to illustrate the effectiveness of proposed framework of algorithms. Further, three component level problems having non-convex domains have also been discussed to establish the robustness and modeling capabilities of the proposed work. A good agreement between the simulated results and reference data demonstrates the algorithm’s competence and robustness for modeling thermoelastic fracture in graded materials. The proposed methodology improves the computational efficiency and flexibility of the element-free Galerkin method for modeling thermoelastic fracture in graded media. Moreover, enhancement of computing speed with the proposed methodology adds to its modeling potential.