Controllable Deformations of Unconstrained Ideal Nematic Elastomers

Abstract

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen’s theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen’s theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart.