In short: Does anybody know if there exists a compendium, a document, a book or a stone tablet listing the independent elements of the elastic stiffness and compliance tensors ( that is, naming the elements, e.g., $C_{1111},C_{2222},\ldots$ that are independent and giving the values of the dependent elements as functions of the independent ones ) for all space groups? Thanks very much!!
In long: Recently I was doing some calculations that involved handling the elastic stiffness tensor from elasticity theory, namely $C_{ijkl}$, for materials with quite specific symmetries. As you probably know, $C_{ijkl}$ has, in general, 21 independent elements. But, depending on the symmetries of the crystal you are regarding, this can change dramatically, down to 2 independent elements for isotropic materials.
I thought to my-self: Well, there is only a finite number of space groups out there, so somebody should have one day calculated the independent elements of $C_{ijkl}$ for all space groups that exist. And, while we are at it, also for its inverse, the compliance tensor $S_{ijkl}$. But I was not succesfull in finding such a compendium anywhere and had to do the calculation on my own. Poor me. Perhaps we can help future generations with that information?