Solid liquid crystals, formed by crosslinking polymeric nematics into
elastomers, display novel and complex elasticity. The internal nematic
direction experiences a barrier to its rotation which couples it to t
he deformations of standard elasticity. Electric fields acting on anis
otropic chains induce orientational torques, which compete with rubber
elastic effects. Outcome structures crucially depend on the mechanica
l constraints applied to the sample. In set-ups with no or few constra
ints, an electric field rotates the nematic director without resistanc
e, inducing also a spontaneous shape change of a rubber or gel matrix.
When certain strains are prevented in the sample by external constrai
nts, the magnitude of the elastic barrier is much higher than the elec
tric contribution and a very high electric field is required to create
an observable director rotation. In weakly anisotropic elastomers, fo
r instance conventional rubbers which have been strained during crossl
inking, the characteristic field will be considerably lower. Experimen
tal observations on nematic gels support our predictions.