Freedericksz instability for the twisted nematic device: A three-dimensional analysis

Of interest here is the fully three-dimensional analysis of the Freedericksz transition for the twisted nematic device (TND), which is widely used in liquid-crystal display monitors. Using a coupled electromechanical variational formulation, the problem is treated as a bifurcation instability triggered by an externally applied electric field. More specifically, we study a finite thickness liquid-crystal layer, anchored between two infinite parallel plates relatively rotated with respect to each other by a given twist angle and subjected to a uniform electric field perpendicular to these bounding plates. The novelty of the proposed analysis lies in the fully three-dimensional formulation of the TND problem that considers all possible bounded perturbations about the principal solution. By scanning a wide range of the liquid crystal's material parameter space, we establish whether the Freedericksz transition is global, i.e., has an eigenmode depending solely on the layer thickness coordinate, or local (also termed the periodic Freedericksz transition), i.e., has an eigenmode with finite wavelengths in one or both directions parallel to the plate. It is found that global modes are typical for low values, while local modes appear at large values of the twist angle. Moreover, for certain TND's, the increase in twist angle can lower the critical electric field, findings that could be useful in guiding liquid-crystal selection for applications.

Nonlinear electro-magneto-mechanical constitutive modelling of monolayer graphene

Using the classical theory of invariants for the specific class of graphene's symmetry, we constitutively characterize electro-magneto-mechanical interactions of graphene at continuum level. Graphene's energy depends on five arguments: the Finger strain tensor, the curvature tensor, the shift vector, the effective electric field intensity and the effective magnetic induction. The Finger strain tensor describes in- surface phenomena, the curvature tensor is responsible for the out-of-surface motions, while the shift vector is used due to the fact that graphene is a multilattice. The electric and the magnetic fields are described by the effective electric field intensity and the effective magnetic induction, respectively. An energy with the above arguments that also respects graphene's symmetries is found to have 42 invariants. Using these invariants, we evaluate all relevant measures by finding derivatives of the energy with respect to the five arguments of the energy. We also lay down the field equations that should be satisfied. These are the Maxwell equations, the momentum equation, the moment of momentum equation and the equation ruling the shift vector. Our framework is general enough to capture fully coupled processes in the finite deformation regime.