The H-microdirectional model: Accounting for a mesoscopic scale

Solving boundary value problems requires implementation of sufficiently robust constitutive models. Most models try to incorporate a great deal of phenomenological ingredients, but this refining often leads to overcomplicated formulations, requiring a large number of parameters to be identified. A powerful alternative can be found with micromechanical models, where the medium is described as a distribution of elementary sets of grains. The complexity is not related to the constitutive description, but to the multiplicity of contacts oriented along all the directions of the physical space. This paper proposes an advanced micromechanical model that introduces an intermediate scale (mesoscopic scale): elementary hexagonal patterns of adjoining particles. This is advantageous with respect to current micromechanical models that generally describe the material through a single distribution of contacts. This new approach makes it possible to take many constitutive properties into account in a very natural way, such as the occurrence of diffuse failure modes. These preliminary results are presented in order to give clear insights into the capability of such multiscale approaches.