An extended element free Galerkin method for fracture analysis of functionally graded materials

An extended element free Galerkin method (XEFGM) has been adopted for fracture analysis of functionally graded materials (FGMs). Orthotropic enrichments functions are used along with the sub-triangle technique for enhancing the Gauss quadrature accuracy near the crack, and the incompatible interaction integral method is employed to calculate the stress intensity factors. Numerical simulations have proved that XEFGM provides more accurate results by less number of nodes (DOFs) in comparison with the unenriched EFGM and other conventional methods for several FGM problems with different crack locations and loadings. The results have been compared with the reference results, showing the reliability, stability, and efficiency of present XEFGM.