Homogenization of an elastic material reinforced by very stiff or heavy fibers. Non-local effects. Memory effects

In a cylindrical domain Omega of R-3, we establish an homogenization result for a boundary value problem of elasticity and for the associated vibration problem. We assume that the data depend in a periodic way on a small parameter E. We assume also that the data take high values on a subset T-epsilon of fibers of Omega such that lim(epsilon-->0) meas(T-epsilon) = 0. We obtain non-local effective laws deduced from a coupled system of partial differential equations; the evolution problem brings to the fore memory effects. (C) 2004 Elsevier SAS. All rights reserved.