Based on granular mesomechanics

this paper sets up the relationship between the macro stress-strain and the mesoscopic quantities including the contact force

contact displacement and branch vector in granular materials. The method of improved Voronoi-Delaunay tessellation for granular materials in geometry and physics is further modified into two cell systems of Bagi. Taking solid cell systems as the basic elements

the average stress tensor that includes particle rotation vector and acceleration of gravity is derived based on Newton’s second law of motion and Gauss theorem. It avoids a static hypothesis. The average strain tensor expression including the void surface vector is derived based on the void cell with compatibility requirement. Two cell systems average equivalent stress-strain is correct combined with the literature of experimental resulting in two dimensions. Compared with two cell systems average equivalent strain and best fitting stress results under three dimensions

granular material stress-strain relationship based on the two cell systems is also validated. Therefore

the granular material stress-strain relationship of the two cell systems provides a theoretical basis for numerical simulation of mechanical properties of granular materials.