Computationally efficient and effective peridynamic model for cracks and fractures in homogeneous and heterogeneous materials

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.