Boundary layer effect at the edge of fibrous composites using homogenization theory

Abstract

Many studies in the theory of composite materials are based on the homogenization approach, which consists of the substitution of the heterogeneous medium by a homogeneous one with certain effective properties. These effective properties are obtained from internal asymptotics which excludes boundary layer effects. However, at the boundary of the individual ply the periodic solution is disrupted. This loss of periodicity of the interior asymptotic solution needs to be accounted for. Here, the boundary layer solution is a correction in the micro solution which accounts for the applied boundary condition. This error gives rise to a sharp boundary layer which decays very quickly when it travels to the interior of the domain, leaving behind a tail which has to be added to the interior solutions to get the correct representation of the global displacement field. It is shown that this correction is significant, local and affects local stress and strain predictions, which are missed by meso or classical micro mechanical solutions. This important outcome of the study proves the theoretical estimates available in the literature (via error estimates in L2 and H1 - norms) emphasizing significant improvement in the local solution at the boundary. It is shown, through numerical examples, that the corrected solution can significantly alter damage initiation predictions at the boundary.