Element-free Galerkin methods for fracture of functionally-graded materials

Since the material properties of the functionally graded materials (FGMs) vary continuously with the coordinates, it is difficult to analyze their mechanical behavior. The conventional finite element method (FEM) treats the nonhomogeneous materials as numerous homogeneous elements, so a very fine mesh is required to analyze FGMs. The element-free Galerkin method (EFGM) adopts the material properties of the integration point when analyzing the homogeneous or nonhomogeneous materials, so it has a good approximation to the actual material properties and requires fewer nodes. In addition, EFGM has no strict element concept and nodes can be distributed freely according to the need without remeshing. The moving least-squares interpolations can produce the continuous results, which have high derivatives. The numerical results show that EFGM has a higher efficiency, accuracy and flexibility to analyze FGMs.