Efficiency has long been a bottleneck for peridynamics simulation as compared to the grid-based methods. This paper proposes a super-fast peridynamic (SFPD) model for crack and fracture simulations in homogeneous and heterogeneous materials in a most efficient manner. The philosophy behind this SFPD algorithm is to decrease the computational time needed at every simulation step rather than to increase the time step, since the peridynamic stability and convergence depend primarily on a small time step. The proposed SFPD algorithm surpasses the classical models and algorithms as follows: (1) the SFPD is hundreds of times faster than the regular peridynamic approach for the same computational task; (2) the peridynamic convergency is dramatically enhanced despite using a smaller number of particles by adopting a new strategy of time step calculation; (3) the SFPD algorithm can simulate the cracks in a wide range of scales including the subatomic scale; (4) the prediction of crack velocity using the SFPD algorithm is much better than other models’ predictions when compared with experimental measurements. Various cracking problems are investigated in both homogeneous and heterogeneous materials under different boundary conditions. The newly proposed algorithm is well-validated to have huge potential in boosting computational efficiency. Moreover, we recommend adopting this algorithm in the software development of crack simulation packages.

与基于网格的方法相比，效率长期以来一直是近场动力学模拟的瓶颈。本文提出了一种超快近场动力学 (SFPD) 模型，用于以最有效的方式模拟均质和异质材料中的裂纹和断裂。这种 SFPD 算法背后的理念是减少每个模拟步骤所需的计算时间，而不是增加时间步长，因为近场动力学稳定性和收敛性主要取决于一个小的时间步长。所提出的 SFPD 算法在以下方面超越了经典模型和算法：（1）对于相同的计算任务，SFPD 比常规的近场动力学方法快数百倍；(2) 近场动力学收敛通过采用新的时间步计算策略，尽管使用较少数量的粒子，但显着增强；(3) SFPD算法可以模拟包括亚原子尺度在内的广泛尺度的裂纹；(4) 与实验测量相比，使用 SFPD 算法对裂纹速度的预测比其他模型的预测要好得多。研究了不同边界条件下均质和异质材料的各种开裂问题。新提出的算法经过充分验证，在提高计算效率方面具有巨大潜力。此外，我们建议在破解模拟包的软件开发中采用该算法。