Exact relations for effective tensors of polycrystals. I: Necessary conditions (Q1282112)

The author describes a general method for finding effective moduli of laminates. The method is applicable to any physical setting that can be put into the Hilbert space framework. The idea is to use the \(W\)-function that transforms a lamination formula into a convex combination. The method reduces the problem of finding exact relations to a problem from representation theory, corresponding to particular physical settings. When this last problem is solved, there is a finite amount of calculations required to be done in order to answer the question completely. The author shows that, at present each candidate relation has to be examined separately in order to confirm the stability under homogenization. Finally, he applies this theory to the determination of conductivity and to the two-dimensional elasticity.