Particulate materials may behave like continuum or non-continuum under various mechanical conditions. Typically there are two ways to connect particulate materials (modeled by Discrete Element Method (DEM)) to their continuum form (modeled by Finite Element Method (FEM)): overlapped/non-overlapped coupling to transition from high-fidelity DEM zone to low fidelity FEM zone, or direct upscaling from particulate materials to continuum (even partially non-continuum). Hereby we attempt to build up a universal mechanism that upscales/maps particulate materials to their continuum form based on large deformation theory, and compute stress, strain, and relevant rate forms in static or dynamic behavior. Fundamental questions should be answered: 1) how the granular stress/strain converge to continuum stress/strain; 2) how the stress, strain and their rate forms are computed and integrated physically in large-scale parallel computing of DEM with non-Lagrangian or Eulerian/non-Eulerian compute grids. Extensive tests ranging from static, medium-rate (gravitational pluviation and collapse), to high rate (oedometer impact, soil-buried explosion, etc) phenomena are investigated to verify the discontinuum-to-continuum upscaling/mapping algorithm, and gain more insight into the mechanical behavior that are not observable without this technique.