This work presents a novel scheme to couple the Discrete Element Method (DEM) and the Boundary Element Method (BEM) for the multi-scale modelling in the time domain. The DEM can model discontinuous material at micro scale very well, but it cannot represent infinite domains. Hence, coupling with the BEM is proposed. A formulation employing the DEM and BEM in different subdomains of the same body is presented. There is no overlap between the sub-domains, and the system of equations is derived based on strong equilibrium and compatibility conditions at the interface. The proposed coupling scheme is based on monolithic time integration. The conducted numerical experiments of one-dimensional wave propagation show excellent agreement with the analytical solution. Some spurious wave reflections are observed at the interface, but their effect is quantified and deemed not critical for infinite domains, which are of main interest. Even though the applications for one-dimensional wave propagation are of limited practical engineering interest, this work represents a significant theoretical breakthrough. This paper establishes a reference for future coupling schemes for two- and three-dimensional multi-scale analysis.

这项工作提出了一种将离散元法 (DEM) 和边界元法 (BEM) 结合起来进行时域多尺度建模的新方案。DEM 可以很好地模拟微观尺度的不连续材料，但它不能表示无限域。因此，建议与边界元耦合。提出了在同一物体的不同子域中使用 DEM 和 BEM 的公式。子域之间没有重叠，方程组是基于界面处的强平衡和相容性条件推导出来的。所提出的耦合方案基于单片时间积分。进行的一维波传播数值实验与解析解非常吻合。在界面处观察到一些杂散波反射，但它们的影响是量化的，并且被认为对于主要感兴趣的无限域并不重要。尽管一维波传播的应用在实际工程中的兴趣有限，但这项工作代表了重大的理论突破。本文为未来二维和三维多尺度分析的耦合方案建立了参考。