Biaxial disclinated states in nematic elastomers

We use a continuum model to investigate the isochoric axial contraction and expansion of a right circular cylindrical specimen composed of a nematic elastomer that is cross-linked in a uniaxial state and then annealed. We build on previous work by relaxing the constraint that the molecular conformation be spherical or uniaxial, allowing instead for biaxiality. The material exhibits an energetic preference for states involving a disclination of strength +1 along the cylinder axis surrounded by a region in which the conformation of the polymer chains is indeed biaxial. We show that such states represent minimizers of the total free-energy. Also, the reactive pressure necessary to enforce the constraint of material incompressibility within the disclination core is found to be reduced by an order of magnitude when the conformation is biaxial rather than uniaxial. A bifurcation analysis is used to analytically determine the thresholds of axial expansion and contraction at which the material prefers a disclinated state. These thresholds are found to be consistent with numerical predictions. Finally, the stability of the solutions for the studied parameters is also investigated.