다중그리드 페리다이나믹 해석법과 다중레벨 손상 매핑을 통한 준정적 취성 균열 전파 해석 기법 연구

초록

Peridynamics is a nonlocal continuum theory based on integro-differential equations without spatial derivatives. Owing to its nonlocality, the implicit formulation for quasi-static crack propagation analysis results in a less sparse system matrix than that for a typical local theory, such as FEM. For efficient matrix calculation, we employ the implicit solution procedure with the multigrid scheme. Failure modeling in peridynamics involves the breaking of the bond between two nodes under a certain damage criterion. Utilizing the sequentially linear analysis (SLA) scheme, this failure model allows for a single bond to be broken at equilibrium points of linear analysis. This makes the entire SLA simulation inefficient. Therefore, a cascadic multigrid scheme is utilized herein to efficiently solve quasi-static problems with the SLA scheme. We also propose a multilevel damage mapping for robust crack propagation in a cascadic multigrid scheme. Further, we present the verification of the robustness of the proposed algorithm based on an m-convergence study.

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