Homogenisation of periodic Cosserat media

Abstract

The present work deals with the development of homogenisation procedures for Cosserat materials with periodic micro-structure. The procedure developed by Forest et al. (2001) for continuum heterogeneous linear elastic Cosserat media is recalled and extended to discrete Cosserat media. The nature of the homogeneous equivalent medium depends on the hierarchy of three characteristic lengths: the size l of the heterogeneities, the Cosserat intrinsic length lc and the typical size L of the considered structure. When l and lc are comparable and much smaller than L, the effective medium is a Cauchy one, whereas the case lc ∼ L leads to a Cosserat effective medium. Applications to square, hexagonal, cubic and tetrakaidecahedral cell micro-structures are provided. We critically address the other existing homogenisation procedures.