The quasiconvex envelope of W

coarse-grains the energetics of the system: it gives the minimum energy needed to produce the macroscopic deformation F, optimized over all possible admissible microstructures y(x). Here the notation means that is Lipschitz-continuous. Note also that the domain , whose volume we denote by , plays here the role of a representative volume element: it can be verified that does not depend on . A function W is quasiconvex if it coincides with its envelope.

The use of in the numerical computations allows one to resolve only the macroscopic length scale, with the (possibly infinitesimal) microscopic scale already accounted for in . Clearly, this approach gives only average information on the fine phase mixtures and focuses on the macroscopic response of the system.