A robust meshfree method for analysis of cohesive crack propagation problems

Abstract In this paper, a new numerical approach is presented for the analysis of cohesive crack propagation in quasi-brittle materials. This approach effectively takes advantage of meshfree radial point interpolation method (RPIM) in conjunction with an accurate integration technique for simulation of cohesive crack growth. Using meshfree methods makes it possible to simply and efficiently model the propagation of the cohesive crack by adding a few number of nodes in the vicinity of the crack tip at each step of crack propagation. Furthermore, a discrete crack can easily be modeled in the meshfree formulation by methods such as visibility criterion. The meshfree method used here is based on the global weak formulation whose domain integrations are calculated with the background decomposition method (BDM). This integration technique can suitably evaluate the domain integrals with high accuracy and minimum computational cost. For the sake of modeling cohesive crack propagation path, consecutive straight segments are used, for each of which interfacial intervals are utilized to apply the constitutive law of cohesive zone. The discretized system of equations for the proposed meshfree method is derived and it is shown how the cohesive forces contribute in generation of the stiffness matrix. Through some numerical examples, the accuracy and efficiency of the proposed method for the analysis of cohesive crack propagation are verified. Also, the accuracy and efficiency of the proposed method are compared to other widely-used numerical schemes. By these examples, the superb efficiency of the presented technique is assessed. Particularly, it is shown that the number of nodes required for achieving accurate results is considerably smaller than other numerical methods such as the extended finite element method XFEM.