PHENOMENOLOGICAL THEORY OF NONUNIFORM NEMATIC ELASTOMERS - FREE-ENERGY OF DEFORMATIONS AND ELECTRIC-FIELD EFFECTS

The general phenomenological free energy is derived for a liquid cryst alline elastomer under arbitrary strain and orientational distortions. Using the group representations method we obtained all invariants, de scribing the coupling of translational and orientational deformations and/or external electric field. It is shown that in centrosymmetric ma terials (nematic rubbers) the only contribution to the free energy whi ch is linear in (small) gradients of the director, is the coupling wit h electric field and the strain tensor (16 independent terms analogous to the flexoelectric effect). In chiral materials (cholesterics) the electric field couples with the strain tensor for uniform nematic dire ctor (piezoelectric effect, 3 invariants) and, in the absence of an el ectric field, translational and linear orientational distortions inter act with each other (couple-stress effects, 6 invariants). Experimenta l observations and previous models are critically analysed.