Theory of orientational elasticity

In order to describe the local orientation of a macroscopic medium with broken rotational symmetries, an orientational field that consists of three orthonormal vectors is introduced. Next, the deformation free-energy density is constructed and a detailed acount is given of the form and number of the appearing surface terms. It appears that the general expression involves 39 bulk elastic constants and 24 surface elastic constants for nonchiral materials, whereas the property of chirality introduces an additional number of six bulk elastic constants and three surface elastic constants. The influence of discrete and continuous symmetries on the independence of these elastic constants is considered.