Finite block method in fracture analysis with functionally graded materials

The finite block method (FBM) is developed to determine stress intensity factors with orthotropic functionally graded materials under static and dynamic loads in this paper. By employing the Lagrange series, the first order partial differential matrix for one block is derived with arbitrary distribution of nodes. The higher order derivative matrix for two dimensional problems can be constructed directly. For linear elastic fracture mechanics, the COD and J-integral techniques to determine the stress intensity factors are formulated. For the dynamic problems, the Laplace transform method and Durbin's inverse technique are employed. Several examples are given and comparisons have been made with both the finite element method and analytical solutions in order to demonstrate the accuracy and convergence of the finite block method.