Abstract: Quasi-static deformation of granular materials was examined by performing discrete element simulations on polydisperse systems of elastic-perfectly plastic spheres in a periodic cell.Results of simulations of unaxial compression and decompression tests were reported for a 3D system of elastic-perfectly plastic spheres.Based on the theoretical contact mechanics,the numerical simulations demonstrated that the axial stiffness during compression was sensitive to both the amount of plastic deformation and the interparticle friction occurring at the contacts within the assembly of particles.However,the interparticle friction did not appear to have a significant effect on the magnitude of the lateral stress developed during the uniaxial compression.Discrete element simulation also permitted a detailed examination of the evolution of internal variables associated with the micromechanical processes occurring at the particle scale.In this context,the evolution of the induced structural anisotropy,the percentage of sliding contacts,and the average coordination number were presented and discussed.It was shown that at all stages of unloading,interparticle sliding occurred,the number of interparticle contacts reduced and irrecoverable deformation of the microstructure occurred.Consequently,although the initial part of the unloading stress-strain curve might be approximately linear,this did not mean that the system response was elastic,as frequently assumed in continuum theories.