Abstract: In this article, we consider variational inequalities arising, e.g., in modelling diffusion of substances in porous media. We assume that the media fills a domain ?? of ? n with n???3. We study the case where the number of cavities is large and they are periodically distributed along a (n???1)-dimensional manifold. ? is the period while ?? is the size of each cavity with ????1; ? is a parameter that converges towards zero. Moreover, we also assume that the nonlinear process involves a large parameter ??? with ??=?(????1)(n???1). Passing to the scale limit, and depending on the value of ?, the effective equation or variational inequality is obtained. In particular, we find a critical size of the cavities when ??=???=?(n???1)/(n???2). We also construct correctors which improve convergence for ????(n???1)/(n???2).

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