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the study of the behavior of a functionally graded material with interface cracks are facilitated with a new Voronoi Cell Finite Element Method (VCFEM),considering the matrix-inclusion interfacial fatigue crack and matrix fatigue crack.In the new element,all possible contacts on the crack edge are considered by contact seeking and remeshing methods,when the crack is closing under all possible changing loads.The fatigue crack initiates when the fatigue damage exceeds certain critical damage value,and fatigue crack propagation are simulated by gradual seeking crack propagating directions and new crack tips,using a remeshing method that a damaged node at the crack tip is replaced by a pair of nodes,a new crack tip node is assigned at the crack propagating directions and a more pair of nodes are needed to be added on the crack edge near the crack tip in order to better facilitate the free-traction boundary condition.The first example has been given for Particlereinforced metal-matrix composites with 20 elliptical inclusions to simulate the fatigue crack initiation and propagation under plane stress conditions.It appears that this method is a more efficient way to deal with the interfacial damage of composite materials.In the second example,the results show that the mechanical properties of functionally gradient materials are influenced by the particles’ size,topological structure,and interfacial deboning strength.With the interface cracking the overall stiffness of functionally gradient materials is gradually reduced.