Scale-size effects analysis of optimal periodic material microstructures designed by the inverse homogenization method

Abstract

Periodic homogenization models are often used to compute the elastic properties of periodic composite materials based on the shape/periodicity of a given material unit-cell. Conversely, in material design, the unit-cell is not known a priori, and the goal is to design it to attain specific properties values – inverse homogenization problem. This problem is often solved by formulating it as an optimization problem. In this approach, the unit-cell is assumed infinitely small and with periodic boundary conditions. However, in practice, the composite material comprises a finite number of measurable unit-cells and the stress/strain fields are not periodic near the structure boundary. It is thus critical to investigate whether the obtained topologies 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 apparent properties of the resulting composite by means of standard numerical experiments.