EXACT RELATIONS FOR EFFECTIVE TENSORS OF POLYCRYSTALS - II - APPLICATIONS TO ELASTICITY AND PIEZOELECTRICITY

An important necessary condition for an exact relation far effective m oduli of polycrystals to hold is stability of that relation under lami nation. This requirement is so restrictive that it is possible (if not always feasible) to find all such relations explicitly. In order to d o this one needs to combine the results developed in Part I of this pa per and the representation theory of the rotation groups SO(2) and SO( 3). More precisely, one needs to know all rotationally invariant subsp aces of; the space of material moduli. This paper presents an algorith m for finding all such subspaces. We illustrate the workings of the al gorithm on the examples of 3-dimensional elasticity, where we get all the exact relations, and the examples of 2-dimensional and 3-dimension al piezoelectricity, where we get some (possibly all) of them.