Computational models of periodic composites. Tolerance averaging versus homogenization

Physical reliability of the known asymptotic homogenization models of periodic composites is discussed. By retaining some terms which are neglected in the homogenization a refined approach to the modelling of composites is proposed. It is shown that this approach results in the non-asymptotic tolerance averaged models which for special problems coincide with the homogenized ones but also are able to describe physical situations which are outside the framework of homogenization theory. The analysis is carried out for the heat conduction problem.