Computation of coarse grain structures using a homogeneous equivalent medium

This paper deals with the improvement of concentration relations when some basic hypothesis of homogenization techniques are no longer valid inducing important errors in the deduced local fields. In the first part of this wor k we propose a new formalism of the standard concentration rules developed in the homogenization of periodic media framework. In a second part; we ins ist on the fact that a homogeneous equivalent medium replacing a coarse gra in material is in fact expected to be a generalized continuum. Additional s tiffnesses must be attributed to the unit cell and special non-homogeneous boundary conditions and their periodic counterparts are proposed. The resul ting HEM turns out to be a Cosserat continuum.