On the definition of a relevant meso-scale for upscaling the mechanical behavior of 3D granular materials

In this paper, the difficulty to adapt the definition of a meso-scale for 2D granular materials to derive the macroscopic mechanical behavior of 3D granular materials by upscaling is discussed. A starting point for a definition of a 3D meso-scale may be found in previous works where the transport of small particles through a set of defined pores and constrictions has been investigated. In this framework, different methods to derive a set of pores on which can be defined 3D meso-domains have been compared. Some clues are given about their relevancy to address the macroscopic mechanical behavior of 3D granular materials using an upscaling from a meso-scale. Graphic abstract