Extended scheme for the projection of material tensors of arbitrary symmetry onto a higher symmetry tensor

I propose a straightforward generalization of the projection scheme for elastic tensors introduced by Moakher and Norris [J. Elasticity 85, 215 (2006)] that takes into account also rotations. The "closest" tensor of any desired symmetry to the original tensor of lower symmetry is "closer" in this generalized scheme. The method has an important application in the context of the special quasirandom structure (SQS) method for the computational modeling of alloys, whereby the supercell's symmetry, and therefore that of the tensors representing its properties, is reduced with respect to the material's underlying symmetry. The approach allows to extract the tensor components most representative of the macroscopic symmetry of the material. Although the approach is general, in the present case I apply it to the elastic tensor and give numerical examples. Simple approximate analytical expressions for cubic materials are also provided.