This paper intends to propose a new micro-mechanical definition of strain tensor for granular materials, using the Dirichlet (or modified Voronoi) tessellation defined for granular assemblies. Although another definition of strain tensor has been proposed up to the present, it is shown that the new definition has a lot of advantageous points, such as the good correspondence to the compatibility condition. Regarding the most general case, the micro-mechanical definition is also given for couple stress and rotational strain. For the inner work in granular materials, it is shown that the proposed strain satisfies the Hill's condition in a modified and radical form. To clarify the necessity of the micro-mechanical strain, three kinds of simple shear deformation, which are same macroscopically but different micro-mechanically, are analyzed using the proposed strain definition.
