Elastic Constants of 3D Anisotropic Fluids

In this coordinate system the director curvature can be separated into six components  

Representation of the director deformation field for splays, twists and bends. 

In the limit of small distortions aVn 1 a molecular size), the distortion free energy density approaches zero, which means that F can be expressed in powers of Viz. 

as usual, summation over repeated suffices is implied. So far, we did not have any symmetry considerations, so (C.5) would mean that we need to deal wilh 36 + 6 elastic constants, which would make any analysis extremely complicated. Fortunately, the symmetry of the material reduces the nmnber of nonzero elastic constants considerably. 

Because there was arbitrariness in om choice of coordinate system, we require that when we replace this by other permissible one (x, y, z ), in which we have new curvature elastic components, F should be the same as before. As the Curie principle states, this implies that the same conditions will be valid for the elastic constants determined by a, and aflj as for those determined by a and a/Uj.  

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