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

Abstract

The non-locality property of peridynamic poses significant computational challenges, especially for problems with discontinuous solutions (e.g., cracks). An efficient matrix-structure-based fast (MSBF) algorithm is proposed for the meshfree method (MF) in solving the linearized bond-based peridynamic models on a rectangular Cartesian computational domain with a uniform mesh. Taking full advantage of the intrinsic Teoplitz structure of the block-diagonal stiffness matrix, the fast Fourier transform (FFT) algorithm is utilized to significantly reduce the number of floating point operations (FLOPS) count to achieve a substantial speed up at fine mesh resolutions than the classical matrix-vector multiplication (MVMP) algorithm. Both methods are applied to multi-dimensional static and dynamic problems, including general boundary conditions and unsteady crack propagation, with good results. The MF-MSBF algorithm demonstrates its substantial computational efficiency with greatly reduced CPU times and smaller memory footprint over the MF-MVMP algorithm in multi-dimensional peridynamic simulations with fine meshes.