On the definition of an average strain tensor for two-dimensional granular material assemblies

The description of deformation of granular assemblies is one of the basic ingredients, in view of developing constitutive relations following a micromechanical line. Ignoring the deformation of particles, the macroscopic strain of a granular specimen results from the relative motions of particles, including both translational and rotational kinematics. This paper investigates to which extend the rotation of grains should be accounted for in the description of macroscopic strains, depending on the size of (that is, the number of particles in) the granular specimen. Some examples of simple two-dimensional granular assemblies of circular grains are considered and discussed to illustrate the general results derived from a micromechanical approach.