Numerical simulation of adiabatic and isothermal cracks in functionally graded materials using optimized element-free Galerkin method

In the present work, element-free Galerkin method (EFGM) is modified and implemented to simulate thermoelastic fracture in functionally graded materials (FGMs). By solving the simple heat transfer problem, the temperature distribution over the domain can be obtained which is later used as an input to determine the displacement and stress fields. The crack surfaces are modeled under adiabatic and isothermal conditions. To capture stress fields around the crack tip, intrinsic enrichment criterion is used. A modified conservative M-integral technique has been used to extract the stress intensity factors (SIFs) for the simulated problems. A new algorithm to ensure equal number of nodes in support domain has been suggested. The optimum size of support domain is derived by performing an optimization of predefined EFGM parameters, namely, total number of nodes in problem geometry, Gauss quadrature, and number of nodes in support domain. Taguchi L-16 orthogonal array is used to obtain optimized values of these parameters. The results of analysis by optimized EFGM (OEFG) show about 80% reduction in computational time and an improvement in accuracy over EFGM. The present analysis shows that the results obtained by OEFG are in good agreement with those available in the literature.