The GW model is better suited for lightly loaded contacts with large separations where the surface asperities deform elastically as the Hertz contact model is adopted for the contact load calculation between the asperity and the sphere. When a positive overlap is involved in the contact, it may be necessary to consider the plastic deformation of the surface asperities. Over the last three decades, several elasto–plastic contact models have been developed for rough surfaces. Based on the concept of volume conservation, Chang et al. [28] propose the CEB model in which a critical interference (or overlap) divides the contact regime into elastic and fully plastic components. By recognizing the discontinuity involved in the average contact pressure at the critical point of the plastic deformation in the CEB model, Zhao et al. [29] present a new elastic-elasto/plastic-fully plastic model (termed the ZMC model) which introduces two critical interferences and bridges the elastic and plastic behavior of the asperity using a cubic polynomial. In addition, based on the work of Kogut and Etsion [30,31], the finite element analysis has been applied to treat different deformation regimes under which several useful empirical elasto–plastic models have been derived [32,33]. In addition to the above work that are mainly presented in the tribology literature to treat the plastic deformation involved in contact problem of rough surfaces, there are also a number of elasto–plastic models proposed for contacting (smooth) spheres in DEM [34–41]. By considering both advantages and disadvantages of these models, an extended elasto–plastic GW (EP-GW) model is also developed in the current work to fully take into account the plastic deformation of the asperities.