Homogenized equation of second-order accuracy for conductivity of laminates

Abstract

The high order homogenization techniques potentially generate the so-called innite order homogenized equations. Since long ago, the coecients at higher order derivatives in these equations have been calculated within various rened theories for both periodic composites and thin structures. However, it was not always clear, what is a wellposed mathematical formulation for such equations. In the present paper we discuss two techniques for constructing a second order homogenized equation. One of them is concerned with the projection of a weak formulation of the original problem on an "ansatz subspace".The second one corresponds to the traditional two scale asymptotic expansion using representation of a second order corrector via the solution of the classical (leading order) homogenized equation.