Elasticity of Smectic A Phase

This means that the only term remaining in the free energy density is  

In case of sufficiently strong director bend, we will create defects (see Chapter 6) edge dislocations will invade the smectic in an attempt to keep the layer thickness constant. 

The layers will be compressed or dilated if du/dz 0. We assume that there is a linear relation between the stress and strain across the layers. The corresponding term in the elastic energy then will be, where B is the layer 

if the displacement varies along 2, two additional terms proportional to d u/dz vdll appear, too. They, however, practically always can be neglected. 

The eqiiilibrium structures are detenriined by the condition that J FddV should be minimal. This is the problem of variation calculus, and the solution is given by the Euler-Lagrange equation. Assuming uniformity in y direction  

---