Exact connections are shown to exist between the properties of two-dimensional polycrystalline aggregates and those of its constituent elongated crystals. The analysis is given for piezoelectric crystals and polycrystals. Both the crystal and the polycrystal are assumed to belong to the 2 mm class of the orthorhombic system. Classes that are special cases of 2 mm crystals are also admitted. The corresponding results for purely elastic aggregates, hitherto unknown, are obtained as a special case. The majority of the derived results are an outcome of uniform fields in the polycrystals considered, whose existence is established in this paper. In addition, these fields allow the derivation of certain correspondence relations between the pointwise local fields in the polycrystal, when it is subjected to certain electromechanical loadings. Exact connections for a subclass of the effective constants which are not amenable to the uniform field analysis are obtained by a matrix diagonalization formalism. It is shown that uniform fields and local correspondence relations exist also in three-dimensional elastic polycrystalline aggregates with tetragonal, hexagonal or trigonal crystals.
Ramification theory for higher dimensional local fields
