Many people are convinced that they know and understand the subject of composite engineering, its design purposes and procedures. A customer usually wants just "these properties", while a manufacturer's goal is to be able to answer that he, of coarse, can do the material with these and more than "these properties." The burden of proof is on shoulders of designers, composite engineers. As long as they know by training, they do the modeling and the design using the one scale methods. It is known, meanwhile, that composite materials mostly can not be considered as a perfect mixtures, chemically bonded on the molecular scale.
We would consider here the few related, but taken separately two- (or more) scale problems for heterogeneous composites:
The two latter problems are the pretty well known tasks and one might ask - what the heck you would disclose to us that we haven't already known?
Well, I would answer that I am not going to repeat the well known statements and their solutions (just mentioning few of them), instead I would, of coarse, talk about the Scaling treatment of these problems, the HSP-VAT formulations, and just something about the HSP-VAT solutions. Because these solutions so far mostly have not been seen around, at least in textbooks, and in official university courses, etc. To provide the correct scaled solutions for these problems we have done a lot of work.
Meanwhile, these studies are too costly, and too scarce are the resources so far. The workload for solving these problems (apart of a number of people who know How to solve the Two-Scale HSP-VAT problem) approaching to the amount of work usually provided for the MHD tasks. Have anyone saw the fusion studies papers or reports made by one-two-three people? Hardly, right? There is the opinion that this is the way things should not be done and in Scaled heterogeneous physics to reach the goals, with the highest reward.
We believe that the scaled approach is the answer - these tasks, in either way have been formulated via one or another subconscious way for seeking the solution and their summaries on the upper scale, but then inevitably were being solved on the lower scale with consecutive attempts of making rude and often incorrect statistical or spatial averaging for the Upper scale goals proclaimed.