How to determine composite material properties using numerical homogenization

• Educational paper covering implementation of numerical homogenization.
• Examples include elasticity, conductivity, thermal expansion, and fluid permeability.
• It is shown how to easily extend the implementation from a two material composite to include more materials.
• The representative volume element can be a square, rectangle, or parallelogram, allowing for all kinds of 2D periodicities.
• The implementation is a compact Matlab function provided in the appendix.

Numerical homogenization is an efficient way to determine effective macroscopic properties, such as the elasticity tensor, of a periodic composite material. In this paper an educational description of the method is provided based on a short, self-contained Matlab implementation. It is shown how the basic code, which computes the effective elasticity tensor of a two material composite, where one material could be void, is easily extended to include more materials. Furthermore, extensions to homogenization of conductivity, thermal expansion, and fluid permeability are described in detail. The unit cell of the periodic material can take the shape of a square, rectangle, or parallelogram, allowing for all kinds of 2D periodicities.