Anisotropic elastic constants that are structurally invariant

A set of anisotropic elastic constants is said to be structurally invariant if, under an orthogonal transformation of the coordinate system, the zero elements remain zero and certain relations between the elements are preserv ed. The elastic constants of an isotropic elastic material are structurally invariant under any orthogonal transformation. In fact they are invariants . We will show that they are not the only ones that are structurally invari ant for a three-dimensional transformation. For a two-dimensional transform ation for which the coordinate system is rotated about the x(3)-axis by an angle, we show that there are eleven structural invariants. Monoclinic mate rials with the symmetry plane at x(3) = 0 have three structural invariants while transversely isotropic elastic materials with the x(3)-axis as the ax is of symmetry have seven structural invariants. The results are useful in analysing layered composites such as layered plates or shells for which eac h layer is of the same material but the layers are rotated with respect to each other by an angle. It is also useful for a continuously twisted struct urally chiral medium.