The current work is part of an ongoing effort to couple the Discrete Element Method (DEM), used as a mesoscale method, with Statistical Mechanics in order to construct a framework for the modeling, homogenization, and uncertainty quantification of particulate geomaterials. The aspect of the framework tackled in this work, is the quantification of stress and deformation of heterogenous DE models. Such quantification is necessary to allow DEM to “speak continuum”. DEM is a discrete particle method, wherein the concept of “stress” does not fit naturally, but where each particle pair is considered to interact through discrete forces. Additionally, DEM is an explicit method, and equivalent continuum deformation must be defined in the context of particle kinematics.