Asymptotic analysis of heterogeneous Cosserat media

The present work deals with the development of homogenization procedures fo r periodic heterogeneous linear elastic Cosserat media. It is resorted to a symptotic methods classically used in periodic homogenization. It is shown that the nature of the homogeneous equivalent medium depends on the hierarc hy of three characteristic lengths: the size l of the heterogeneities, the Cosserat intrinsic lengths l(c) of the constituents and the typical size L of the considered structure. When l and l(c) are comparable and much smalle r than L, the effective medium is proved to be a Cauchy continuum with volu me couples, whereas the case l(c) similar to L leads to a Cosserat effectiv e medium. Finite element simulations are provided in the case of a fiber-ma trix composite for a large range of characteristic lengths l(c) and for two different volume fractions. Reference calculations involving every heterog eneity are compared to the response obtained using a homogeneous equivalent medium. The results confirm the predicted hierarchy of models and also sho w that a Cosserat effective medium still provide a good estimation when all characteristic lengths have the same order of magnitude. (C) 2001 Elsevier Science Ltd. All rights reserved.