Homogenization theory and multiscale numerical approaches for random media

We will overview a series of recent works [1, 2, 3, 4, 5, 6, 7] all related to some multiscale problems motivated by practical problems in Mechanics. The common denominator of all these works is that they address multiscale problems where the geometry of the microstructures is not periodic. Random modelling, but not only (see e.g. [2, 3]), can then be used in order to account for the imperfections of the medium. The theory at play is that of homogenization, in its many variants (stochastic, general deterministic, periodic). The numerical methods developed and adapted are finite element type methods.