Two-grid based sequential peridynamic analysis method for quasi-static crack propagation

Abstract

We introduce two-grid based sequential analysis algorithm for implicit peridynamics to find the quasi-static solutions for crack propagation problems. The sequential analysis of implicit peridynamic formulation is capable of studying quasi-static fracturing of brittle materials. The failure model in peridynamics, however, usually allows one to break a single bond between two nodes under a certain damage criterion in tracing equilibrium points, which results in the whole simulation quite lengthy and inefficient. In order to circumvent the efficiency issue, we propose the two-grid based sequential peridynamic analysis algorithm, in which a coarse grid is used to find the equilibrium path with sequential analysis and the converged solution is properly prolongated to the fine grid. The failure model is also implemented in the coarse grid and the computed damage information is properly mapped into the fine grid. In this way, the proposed two-grid based scheme incorporates breaking multiple bonds into one step of sequential analyses. We document the superior behavior of the proposed scheme with respect to the conventional solution procedures of implicit peridynamics in both solution accuracy and computational efficiency for quasi-static crack propagation. © 2022 Elsevier Ltd