Abstract: The traditional peridynamics method replaces partial differential equations in continuum mechanics with integral equations, resulting in more generalized equations without smoothness restrictions on the unknown function. This makes the methodology particularly suitable for simulating discontinuous problems, such as spontaneous crack initiation and propagation. However, the high computational cost often limits its practical engineering applications. This paper introduces a fast convolution-based method for peridynamics to enhance computational efficiency. This algorithm employs fast Fourier transformation to accomplish convolution calculations, facilitating the computation of integral terms in peridynamics equations, significantly reducing the computational cost of the peridynamics method. A preprocessing method suitable for this algorithm is proposed based on the computational process and numerical implementation characteristics of the fast convolution-based method for peridynamics. Its feasibility is verified through two tensile square plate examples with pre-existing cracks. Furthermore, a modeling method for predicting random crack propagation is proposed, offering a novel approach for research in predicting random crack propagation in geomaterials.

Key words: peridynamics, fast convolution, modeling method, random crack propagation prediction