An adaptive partitioned reduced order model of peridynamics for efficient static fracture simulation

Abstract

In this paper, an adaptive partitioning strategy and the proper orthogonal decomposition–Galerkin method are combined to formulate an adaptive partitioned reduced order model (APROM) for fast solution of peridynamic (PD) models involving fractures. A boundary layer separation approach is presented to tackle the inaccurate reproduction of nonlocal boundary conditions in the reduced order model (ROM). Cracks invariably make ROM results more sensitive to the snapshots, i.e. a set of high-fidelity solutions simulated by the full order model (FOM), and this challenge is overcome by an adaptive partitioning strategy. The internal computational domain is divided into two parts: the crack region is modeled by full PD model, and the remaining region is dimensionally reduced. The partitioned configuration is automatically updated with the damage evolution. Several numerical tests are executed to verify the performance of the APROM, which shows that the APROM is able to successfully simulate various fracture phenomena. A significant improvement in computational efficiency is found: the number of degrees of freedom in the full PD model is greatly reduced, leading to an approximately 10 times improvement in CPU time without loss of accuracy. This paper provides strong theoretical support for accelerating PD solutions, thereby promoting the practical application of PD theory in large-scale engineering projects.