DEM-BEM coupling in time domain for one-dimensional wave propagation

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.