Ordinary state-based peridynamic (OSB-PD) models have an unparalleled
capability to simulate crack propagation phenomena in solids with arbitrary
Poisson's ratio. However, their non-locality also leads to prohibitively high
computational cost. In this paper, a fast solution scheme for OSB-PD models
based on matrix operation is introduced, with which, the graphics processing
units (GPUs) are used to accelerate the computation. For the purpose of
comparison and verification, a commonly used solution scheme based on loop
operation is also presented. An in-house software is developed in MATLAB.
Firstly, the vibration of a cantilever beam is solved for validating the loop-
and matrix-based schemes by comparing the numerical solutions to those produced
by a FEM software. Subsequently, two typical dynamic crack propagation problems
are simulated to illustrate the effectiveness of the proposed schemes in
solving dynamic fracture problems. Finally, the simulation of the Brokenshire
torsion experiment is carried out by using the matrix-based scheme, and the
similarity in the shapes of the experimental and numerical broken specimens
further demonstrates the ability of the proposed approach to deal with 3D
non-planar fracture problems. In addition, the speed-up of the matrix-based
scheme with respect to the loop-based scheme and the performance of the GPU
acceleration are investigated. The results emphasize the high computational
efficiency of the matrix-based implementation scheme.Comment: 32 pages, 16 figure