A Continuum Model for Diffusion in Laminated Composite Media

Abstract

Using a method developed for studying wave propagation problems, a continuum theory is developed for diffusion-type processes in a laminated composite with periodic micro-structure. Construction is based upon an asymptotic scheme in which a typical macrodimension is assumed large compared to a microdimension. The order of truncation of the asymptotic sequence so obtained defines a hierarchy of models. Solutions are given for the lowest-order models and compared with the results from a finite difference code. For most cases the zeroth-order “effective conductivity” theory yields good results. For exceptional problems requiring a higher-order theory, a modified version of the first-order theory is shown to suffice. For many applications these elementary equations may offer an attractive alternative to other means for obtaining solutions.