Swelling and tilting in smectic layers

Smectic liquid crystals are quasi-solid materials, in that they possess microstructure both of the material and the local type (the nematic microstructure and the lamellae). In the standard approach, the rod-like molecules are supposed to be strictly normal to the layers; here we abandon this constraint and admit the possibility for the molecules to change orientation with respect to the layers, paying in energy. As a consequence, we obtain two equations: one expresses the balance of micromomentum, the other is Cauchy's equation. We derive also their form in the linear approximation and solve two typical problems.