Fracture modeling of isotropic functionally graded materials by the numerical manifold method

Two-dimensional stationary cracks in isotropic functionally graded materials (FGMs) are studied by the numerical manifold method (NMM). The near-tip behavior of a crack in FGMs is manifested by a special choice of cover functions, and the displacement jump across a crack face is naturally represented taking the benefit of the NMM. The stress intensity factors (SIFs) are computed by the equivalent domain form of the interaction integral using the nonequilibrium auxiliary fields. Typical examples involving single- and multi-branched crack are conducted to verify the accuracy of the proposed method. Problems are tackled with the uniform mathematical cover system independent of the physical boundaries and the calculated SIFs match well with the existing reference solutions.