Fracture analysis employing equivalent domain integral method and nodal integration techniques based on reproducing kernel particle method

A novel technique to evaluate fracture mechanics parameters is investigated employing the equivalent domain integral (EDI) method and nodal integration (NI) techniques. Galerkin-based meshfree method is adopted. Reproducing kernel (RK) is chosen for the meshfree interpolant. Stabilized conforming nodal integration (SCNI) and sub-domain stabilized conforming integration (SSCI) are adopted for numerically integrating the stiffness matrix. Voronoi diagram is employed to compute volume of each NI domain. The EDI method is addressed to evaluate the fracture mechanics parameters, i.e., energy release rate and stress intensity factors (SIFs). Because the displacement and its derivatives are computed based on SCNI/SSCI, the EDI can be discretized by summing up the physical quantities and volume of each cell/sub-cell. No special quadrature rule is required. To separate the energy release rate into the mixed-mode SIFs, interaction integral method is chosen. Efficient and accurate fracture parameter computation is achieved. Some numerical examples are demonstrated for mixed-mode fracture parameter evaluation and crack propagation analysis. Accuracy and effectiveness of the presented approach are studied.