Simulating quasi-static crack propagation by coupled peridynamics least square minimization with finite element method

Abstract In this work, we present an innovative simulation method for quasi-static crack propagation in mixed-mode, within a new framework of coupled peridynamics least square minimization and finite element method (PDLSM–FEM). As the inertia effect is neglected for quasi-static problems, the governing equations for PDLSM–FEM can be solved implicitly without iterations. Displacements and stresses from PDLSM–FEM are used to compute the interaction integral, an extended version of the J -integral. The stress intensity factors (SIFs) are derived from the interaction integral and used in the maximum circumferential tensile stress failure criterion to predict the onset of crack propagation and the direction of propagation. New contributions in this work include the following: (1) developing a new framework for coupling PDLSM and FEM; (2) pioneering a quasi-static method for simulating crack propagation in peridynamics; (3) developing an element-based approach for selecting the interaction integral contour; and (4) proposing and implementing an innovative method for handling peridynamic bond breakage and crack growth. Quasi-static crack propagation simulation in this work provides a computationally efficient way to find the shape of the crack, and the current PDLSM–FEM model is straightforward and can be easily introduced into commercial finite element codes. Three numerical examples are carried out, and the results show that the proposed method evaluates SIFs accurately and captures crack growth as expected.