The set of effective properties of all possible structures made from
given materials
is called Gclosure of the set of the materials' properties. 
The set of effective properties of all possible structures made from
given materials
taken in given proportions p is called Gpclosure of the set of original properties. 
Why are we interested in the Gclosures?
Mathematically, the problem of bounds and of extremal structures can be formulated as a nonconvex variational problem of minimization of the sum of energies/complimentary energies that a structure stores under different loadings.
We have now a pretty detailed picture of structures of twophase conducting and elastic materials, but the best structures of multiphase composites are mainly unknown.
The difference between twophase and multiphase optimal structures is huge. It is similar to the difference between the black and white and the color TV or between flat and spacial imaging. Multiphase mixtures
The optimal microstructures of multicomponent mixtures are mostly unknown, altough several problems are already solved. The structural variety and the difficulty of the problems are significantly higher then of the twomaterials mixtures.
Jumping from twomaterial structures to multimaterial is like passing from plane to threedimensional world or passing from blackandwhite to color TV.
The next pictures show the variety of the topology of optimal isotropic conducting twodimensional three materials structure. Note the optimal topology of twomaterial mixtures us pretty clear: "good" material outside, "bad" material inside inclusions. In contrast, the optimal topology of threecomponent mixtures depend on their volume fractions.
Isotropic structure of the best conductivity.
Red color corresponds to the best conductor, yellow color  to the intermediate conductor, blue color  to the worst conductor.

