  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.
