Conventional Wisdom

In specifying the stiffness or compliance matrix of an anisotropic material, convention dictates that the coordinate and symmetry systems are aligned to minimize the number of non-zero coefficients; that is, we like to seperate elastic and geometric degrees of freedom. For example, the twelve (nine independent) non-zero coefficients of an orthorhombic system are so  

$$\pmatrix{c_{11}&c_{12}&c_{13}&0&0&0\cr c_{12}&c_{22}&c_{23}... ... 0&0&0&c_{44}&0&0\cr 0&0&0&0&c_{55}&0\cr 0&0&0&0&0&c_{66}\cr}$$ (1)

because we have aligned the coordinate system with the three symmetry axes.