Director reorientation in nematic-liquid-single-crystal elastomers by external mechanical stress

As has been shown recently by Kundler and Finkelmann, a sample of nematic-liquid-single-crystal elastomers subject to a mechanical stress perpendicular to the initial director orientation shows a reorientation of the director reminiscent of that observed in low-molecular-weight nematic liquid crystals in a magnetic field. Here we present a simple model, which captures all the essential features. We calculate the threshold stress and show that the director reorientation occurs over the entire sample. A weakly nonlinear analysis gives a forward bifurcation in agreement with the experimental results. We also discuss the origin of the domain walls in the director observed experimentally and give an expression for the thickness of these walls.