A generalised multi-scale Peridynamics–DEM framework and its application to rigid–soft particle mixtures

The discrete element method (DEM) is the most dominant method for the numerical prediction of dynamic behaviour at grain or particle scale. Nevertheless, due to its discontinuous nature, the DEM is inherently unable to describe microscopic features of individual bodies which can be considered as continuous bodies. To incorporate microscopic features, efficient numerical coupling of the DEM with a continuous method is generally necessary. Thus, a generalised multi-scale PD–DEM framework is developed in this work. In the developed framework, meshfree discretised Peridynamics (PD) is used to describe intra-particle forces within bodies to capture microscopic features. The inter-particle forces of rigid bodies are defined by the DEM whereas a hybrid approach is applied at the PD–DEM interface. In addition, a staggered multi-scale time integration scheme is formulated to allow for an efficient numerical treatment of both methods. Validation examples are presented and the applicability of the developed framework to capture the characteristics mixtures with rigid and deformable bodies is shown.