Generalities on Modeling Problems Involving Multiple Scales

3 Generalities on Modeling Problems Involving Multiple Scales 

Given the examples described in explicit detail above, and by appealing to the examples that have been repeatedly emphasized throughout the book, our present aim is to try to take stock of those features of problems in modeling materials that generically signal the need for some sort of a multiscale approach. In loose terms, it is possible to identify a few different themes that have arisen. 

From a multiple scale modeling perspective, the presence of phenomenological parameters in various effective theories provides an opportunity for information passage in which one theory s phenomenological parameters are seen as derived quantities of another. We have already seen that although the linear theory of elasticity is silent on the particular values adopted by the elastic moduli (except for important thermodynamic inequalities), these parameters may be deduced on the basis of microscopic analysis. The advent of reliable models of material behavior makes it possible to directly calculate these parameters, complementing the more traditional approach which is to determine them experimentally. 

As with most human endeavors, appetite often exceeds capacity. From a computational perspective, despite the staggering increase in computational capacity. 

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