Abstract This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM region for computational efficiency. Within the presented adaptive PDLSM-FEM, only elements intersecting with the crack path and their neighboring elements are defined as PD elements, whose stiffness matrices are derived based on PDLSM equations. The remaining elements are conventional finite elements. Numerical integration of interaction integral is proposed and implemented to evaluate the stress intensity factors (SIFs) for 2-D problems. The criterion of maximum hoop tensile stress is employed for failure prediction. New contributions of this work include the adaptive coupling of PDLSM with FEM for minimizing the PD region and the application of the adaptive PDLSM-FEM to quasi-static crack propagation analysis. Simulations of three 2-D plane stress plates and one 3-D block with static or quasi-static cracks propagation are performed. Results show the proposed method improves computational efficiency substantially and has reasonable accuracy and good capability of crack propagation prediction.
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