13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- reference solutions available showing the implementation effectively to model the discontinuous and to evaluate the SIF. uΓ Node i mi r Node j Neighboring of point x Ci Cj Figure 1. Discrete model of domain 2. The PU-based meshless Shepard interpolation Consider a two-dimensional domain ，and let be discretized by N scattered nodes as shown in Fig. 1. For each nodei , a circle cover (subdomain) } : { mi i r C i x x x , （1） is attached. Here, mi r is the radius of the cover iC . The displacements associated with the node i are denoted by ( , ) 0 0i iu v . For a given point Xሺܺ ∈Ωሻ , based on the PU concept, a new interpolation ݑ ሺܺ ሻ at X can be defined by ݑ ሺܺ ሻൌ∑ ∅ ሺ ݔ ሻ ି ଵ ݑ ሺܺ ሻ （2） where n is the total number of neighboring nodes where the position of point x located in the cover support. ( )x l i u are the cover interpolations defined on the cover of nodei . In MSIM, the interpolations are constructed separately for the nodes on the essential boundary or in the domain.. x 0 i is the Shepard function or zeroth-order function n i i i i w w 1 0 x x x （3） where x iw is the weight function associated with nodei . The Shepard function x 0 i in Eq. (3) satisfies the delta property if weight function is singular at i x x . The weight function[12] adopted here is
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