Conservation equations

Intuitively, we can say that behavior on a global scale corresponds to the average of local behaviors. There are many approaches for arriving at an average macroscopic description from a microscopic one. The most common are the asymptotic method for media with periodic microstructure and the method using volume-averaged operators, which is used in random media where the VER replaces the case of the periodic cell. They share certain principles, such as the prerequisite of strong scale separation, statistical homogeneity of the media and the use of averaging operators to calculate the effective coefficients. Mean-field methods assume the form of the equations at the macroscopic scale, which is not necessary for materials with periodic microstructure. As discussed in section