A fast computational framework for the linear bond-based peridynamic model

TL;DR

This paper introduces a matrix-structure-based fast computational framework for linear bond-based peridynamic models, significantly reducing computational cost and memory usage, and applicable to various 2D/3D problems including crack propagation.

Contribution

It presents a general, efficient computational framework (MSBFM) that overcomes existing limitations, applicable to static/dynamic problems with complex boundary conditions.

Findings

Computational cost reduced from O(N^2) to O(N log N)

Memory requirement reduced from O(N^2) to O(N)

Numerical examples verify efficiency and practicality

Abstract

Peridynamic (PD) theory is significant and promising in engineering and materials science; however, it imposes challenges owing to the enormous computational cost caused by its nonlocality. Our main contribution, which overcomes the restrictions of the existing fast method, is a general computational framework for the linear bond-based peridynamic models based on the meshfree method, called the matrix-structure-based fast method (MSBFM), which is suitable for the general case, including 2D/3D problems, and static/dynamic issues, as well as problems with general boundary conditions, in particular, problems with crack propagation. Consequently, we provide a general calculation flow chart. The proposed computational framework is practical and easily embedded into the existing computational algorithm. With this framework, the computational cost is reduced from $O(N^2)$ to $O(N\log N)$, and the storage request is reduced from $O(N^2)$ to $O(N)$, where N is the degree of freedom. Finally, the vast reduction of the computational and memory requirement is verified by numerical examples.