On the micromechanical definition of macroscopic strain and strain-rate tensors for granular materials

•Explicit micromechanical expressions for the macroscopic deformation gradient tensor.•Definitions for various macroscopic strain and strain-rate measures.•Main results valid both for infinitesimal strains and moderate finite strains.

Studied is the three-dimensional definition of macroscopic kinematical measures for a representative assembly element (RAE) of a dense granular material, which is assimilated to a representative volume element (RVE) filled with a continuum medium. The geometrical transition from an RAE to an RVE is constructed by means of the Voronoi and Delaunay tessellations associated with the grain centers. After establishing the compatibility conditions that the grain center displacements must satisfy, explicit micromechanical expressions are derived for the macroscopic deformation and velocity gradient tensors. Using these expressions, various macroscopic strain and strain-rate tensors are defined as in continuum mechanics.