Abstract:A meshless manifold method (MMM) is presented to analyze the problems of crack propagation, especially the advantages of MMM for irregular cracks. The shape functions in this method are formed by the partition of unity and the finite cover technology,so the shape functions are not affected by discontinuous domains and crack problems can be more properly treated. For strain localization problems,the shape functions can be more effectively established,compared with other methods in which the tips of the discontinuous cracks are not considered. Compared with the conventional numerical manifold method,the shapes of the finite covers can be selected more easily. The finite covers and the partition of unity functions are formed by using the influence domains of a series of nodes with an advantages over the mesh-based numerical manifold method. Compared with the conventional meshless methods,the test functions are not influenced by the discontinuities in the solution domain since finite cover technology is used to overcome some difficulties inherented in the conventional meshless methods. In this paper,the meshless manifold method (MMM) is applied to analyze crack growth in rock samples. The weak solution of the partial differential equation for elasticity are derived using the method of weighted residuals (MWR). Finally,a problem with crack growth under complex stress state is solved with the MMM,the numerical results agree well with the test data,and the validity and accuracy of the MMM are demonstrated.