Nucleation and critical conditions for stripe domains in monodomain nematic elastomer sheets under uniaxial loading

Abstract

Liquid crystal elastomers with mobile liquid crystal moieties display unique mechanical instabilities and domain patterns in the strain-induced director reorientation. Based on a continuum mechanical model, we present a complete Lagrangian description of finite element formulation of LCEs by solving the coupled displacement and director fields within the Lagrangian scheme. The nucleation of the stripe domain and critical conditions for its formation are numerically studied for thin monodomain centimeter-sized sheets. Under orthogonal uniaxial loading tests, micrometer-sized stripe domains nucleate after loading to a critical strain at which a stress peak is observed along with a reduction in the neo-classical elastic energy. Further, we observed increase in the semisoft and the Frank elastic energy as indications of strong and heterogeneous director rotations. When the loading axis was not exactly orthogonal to the initial director, we found that the sample morphology was strongly dependent on the material and geometrical parameters. Strain-induced stripe domains could still be observed in the central region of the sample when the loading axis was nearly at right angle to the initial director. If the angle between the loading axis and the initial director was slightly deviated from the right angle, nearly uniform rotations were observed. The critical angle, beyond which strain-induced stripe domains were observed, could be very close to the right angle for samples with rather small shape anisotropy and relatively large length to width ratio. In such cases, the observation of strain-induced stripe domains was highly sensitive to any possible experimental error in orienting the loading axis at right angle, and minor deviations from the orthogonal loading condition can cause uniform rotations.