Convergence analysis of stress fields to homogenization predictions in optimal periodic composite design

Abstract

Homogenization assumes that a unit-cell of a periodic composite material is infinitely small and it has periodic boundary conditions. In practice, such material comprises a finite number of measurable unit-cells and the stress fields are not periodic near the structure boundary. It is thus critical to investigate in the scope of the present work whether the optimized unit-cell topologies obtained are affected when applied in the context of real composites. This is done here by scaling the unit-cell an increasing number of times and accessing the micro (or local) stresses of the resulting composite by means of standard numerical experiments and comparing them to the homogenization predictions. The outcome indicates that it is sufficient to have a low scale factor to replace the non-homogeneous composite by the equivalent homogeneous material with the stress field computed by homogenization.