We present a model of particle clusters with realistic, complex shapes composed of elementary DEM spheres. The clusters are rigid bodies kept together by piecewise elasto-plastic-attractive forces acting between the spherical components. These bonds are not rigid, allowing the macroscopic structure of the clusters to undergo partial elastic recovery, permanent plastic deformation and even breakage when subjected to external forces. Multiple clusters can also agglomerate due to the attractive nature of the bonds. The choice of the DEM interaction parameters dictates the structure properties and the physical behaviour of the clusters, allowing the control and precise tuning of their attributes. We illustrate the main features of the clusters and derive a simple analytical model connecting the underlying piecewise interaction between the DEM particles and the clusters’ structural properties. We show how to tune these DEM parameters to control the clusters’ shape and internal structure. Moreover, we present a simplified model linking the interaction parameters to the macroscopic response to external compression forces. By tuning these parameters, we show how the clusters transition between plastic deformation and brittle breakage when compressed. Finally, we present applications of the cluster model to the numerical simulations of complex granular systems, such as compaction and tabletting. The aim of the DEM particle cluster model is to enable the numerical modelling of particles with complex shapes able to deform, break and agglomerate into larger bodies. Exploiting the simplicity of the DEM piecewise interactions allows the control of the clusters’ structural and physical properties while keeping the complexity of the model and the computational expenses to a minimum.