ABSTRACT
Chapter 7 began with a discussion of the separation of scales, and then focused on the problem of material properties below the RVE. With reference to equation (7.1) there, our concern was with the left part of that inequality: d < L or d L . The issue we focus on in this chapter is the right part of (7.1): L Lmacro . That is, if the RVE on scale L is not justified, only a random continuum can be used-recall Figure 1(b) of the Preface. As a result, we need to establish some methods to deal with solution of macroscopic boundary value problems having the mesoscale SVE as input. Such problems are necessarily stochastic, and this leads us to a formulation of random fields of material properties from the SVE information, and their input into numerical methods leading then to so-called stochastic finite element (SFE) and stochastic finite difference methods.
