Disclinations in a homogeneously deformed nematic elastomer

We consider the question of whether a nematic elastomer cross-linked in an isotropic state and then subjected to an isochoric, homogenous deformation can exhibit a disclination. The theory that we use allows for the polymer chains that comprise the network to adopt spherical, uniaxial, or biaxial conformations. The conformation is represented in terms of an orthogonal pair of directors and an associated pair of asphericities. A disclination is a tubular region in which the asphericities vanish and the directors are undefined, so that the conformation is spherical and the material appears to be isotropic. We apply the theory to a cylindrical specimen with circular cross-section deformed so that each cross-section becomes an ellipse. Assuming that, when they exist, the directors are parallel to the level sets of the deformation, the governing equations of the theory reduce to a boundary-value problem involving a pair of semilinear elliptic partial-differential equations for the asphericities. Numerical solutions of that problem predict that the specimen can adopt states in which an isotropic tubular core with characteristic cross-section on the order of 10^-2 ??m is surrounded by material in which the conformation is biaxial. Energetic considerations show that, for reasonable choices of the material properties, such states are preferred for strains greater than or equal to 0.7% and thus a...[more]...published or submitted for publicationis peer reviewe