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.

翻译：常规态近场动力学（OSB-PD）模型在模拟任意泊松比固体中的裂纹扩展现象方面具有卓越能力。然而，其非局部特性也导致计算成本极高。本文提出了一种基于矩阵运算的OSB-PD模型快速求解方案，并利用图形处理器（GPU）加速计算。为便于对比验证，同时介绍了基于循环运算的常用求解方案，并开发了基于MATLAB的自研软件。首先，通过悬臂梁振动问题的求解，比较循环与矩阵方案的计算结果与有限元软件所得数值解以验证方案有效性。随后，模拟两个典型动态裂纹扩展问题以说明所提方案在动态断裂求解中的有效性。最后，采用矩阵方案开展Brokenshire扭转实验模拟，实验与数值断裂试件形态的相似性进一步证明了该方法处理三维非平面断裂问题的能力。此外，研究了矩阵方案相较于循环方案的加速比及GPU加速性能，结果凸显了矩阵实现方案的高计算效率。