Soft elasticity in smectic elastomers.

We investigate the soft elastic modes of smectic elastomers, that is shape change without energy cost. We use a microscopic model for their nonlinear elasticity, similar to those used for nematic elastomers. We consider two different phases of smectic elastomer; the biaxial smectic A for a simple illustration, and smectic C phases which are of great practical significance. We show that only one nontrivial trajectory of the director gives soft deformations. We give a geometrical interpretation of this soft elastic mode and give an explicit example.