Homogenization in a simpler way: analysis and optimization of periodic unit cells with Cauchy–Born hypothesis

Asymptotic expansion based homogenization has been widely used to predict the effective macroscopic properties of periodic unit cells (PUCs). In this work, we show that the homogenization process can be done in a much more elegant manner for both continuum and discrete PUCs by taking advantage of the Cauchy–Born’s hypothesis, which is a widely used rule in the area of solid physics to relate the position of the atoms in a crystal lattice and the...