A high-order multi-time-step (MTS) scheme for the bond-based peridynamic (PD) model, an extension of classical continuous mechanics widely used for analyzing discontinuous problems like cracks, is proposed. The MTS scheme discretizes the spatial domain with a meshfree method and advances in time with a high-order Runge-Kutta method. To effectively handle discontinuities (cracks) that appear in a local subdomain in the solution, the scheme employs the Taylor expansion and Lagrange interpolation polynomials with a finer time step size, that is, coarse and fine time step sizes for smooth and discontinuous subdomains, respectively, to achieve accurate and efficient simulations. By eliminating unnecessary fine-scale resolution imposed on the entire domain, the MTS scheme outperforms the standard PD scheme by significantly reducing computational costs, particularly for problems with discontinuous solutions, as demonstrated by comprehensive theoretical analysis and numerical experiments.

翻译：本文提出了一种面向基于键的近场动力学（PD）模型的高阶多时间步长（MTS）方案。PD模型是经典连续力学的扩展，广泛应用于裂纹等不连续问题的分析。该MTS方案采用无网格方法离散空间域，并使用高阶龙格-库塔方法进行时间推进。为有效处理解中局部子域出现的不连续性（裂纹），方案利用泰勒展开和拉格朗日插值多项式，分别对光滑子域和不连续子域采用粗、细两种时间步长，从而实现精确且高效的模拟。通过避免对整个域施加不必要的细尺度分辨率，该MTS方案相较于标准PD方案，在显著降低计算成本方面表现更优，尤其适用于具有不连续解的问题。综合理论分析与数值实验均验证了这一点。