Title: Homogenisation of periodic Cosserat media

Authors: K. Sab, F. Pradel

Addresses: Institut Navier, LAMI (ENPC/LCPC), Ecole Nationale des Ponts et Chaussees, 6 et 8 avenue Blaise Pascal, 77455, Marne-la-Vallee Cedex 2, France. ' Applied Mechanics Division, Institut Francais du Petrole, 1 et 4 avenue de Bois-Preau, 92852, Rueil-Malmaison Cedex, France

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 l_c and the typical size L of the considered structure. When l and l_c are comparable and much smaller than L, the effective medium is a Cauchy one, whereas the case l_c ∼ 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.

Keywords: homogenisation; micropolar theory; periodic lattices; cellular materials; Cosserat materials; microstructure.

DOI: 10.1504/IJCAT.2009.022703

International Journal of Computer Applications in Technology, 2009 Vol.34 No.1, pp.60 - 71

Published online: 25 Jan 2009 *

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