Continuum theory of elasticity and piezoelectric effects in smectic A elastomers

E.M. Terentjev; M. Warner

doi:doi:10.1051/jp2:1994118

Numéro		J. Phys. II France Volume 4, Numéro 1, January 1994


Page(s)		111 - 126
DOI		https://doi.org/10.1051/jp2:1994118

DOI: 10.1051/jp2:1994118
J. Phys. II France 4 (1994) 111-126

Continuum theory of elasticity and piezoelectric effects in smectic A elastomers

E.M. Terentjev and M. Warner

Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, Great-Britain

(Received 30 July 1993, accepted 6 October 1993)

Abstract
The general continuum free energy is derived for a liquid crystalline (smectic) elastomer under small strain and orientational distortion. Using group representation theory we obtain all invariants describing the coupling of translational and orientational degrees of freedom. Possibilities of uniform rotation of the layer system under shear deformation are outlined. It is shown that in centrosymmetric materials (smectic A) the only polarizational response is flexoelectric, that is in the response to non-uniform orientational deformations. Chiral materials (rubbers of smectic A $^\ast$ ) also have a uniform piezoelectric effect in response to a shear deformation, or an extension at an angle with the layer normal. Possible experimental configurations to observe some of the predicted effects are briefly discussed.