Total Internal Reflection in a Hybrid Nematic Cell Submitted to Weak Boundary Conditions

We calculate the trajectory of a monochromatic optical beam propagating in a planar-homeotropic hybrid nematic crystal cell submitted to weak anchoring conditions. We apply a uniform electric field perpendicular to the cell to control the trajectories for various values of the anchoring elastic energy. We have found that the anchoring energy has a strong influence on the ray penetration length and trajectory. Our calculations are consistent with a previously found Frederick’s type transition only present for weak anchoring in which electric fields above an anchoring-energy dependent critical field align completely the director field.

Elasticity Solutions to Nonbuckling Serpentine Ribbons

Stretchable electronics have found wide applications in bio-mimetic and bio-integrated electronics attributing to their softness, stretchability, and conformability. Although conventional electronic materials are intrinsically stiff and brittle, silicon and metal membranes can be patterned into in-plane serpentine ribbons for enhanced stretchability and compliance. While freestanding thin serpentine ribbons may easily buckle out-of-plane, thick serpentine ribbons may remain unbuckled upon stretching. Curved beam (CB) theory has been applied to analytically solve the strain field and the stiffness of freestanding, nonbuckling serpentine ribbons. While being able to fully capture the strain and stiffness of narrow serpentines, the theory cannot provide accurate solutions to serpentine ribbons whose widths are comparable to the arc radius. Here we report elasticity solutions to accurately capture nonbuckling, wide serpentine ribbons. We have demonstrated that weak boundary conditions are sufficient for solving Airy stress functions except when the serpentine’s total curve length approaches the ribbon width. Slightly modified weak boundary conditions are proposed to resolve this difficulty. Final elasticity solutions are fully validated by finite element models (FEM) and are compared with results obtained by the curved beam theory. When the serpentine ribbons are embedded in polymer matrices, their stretchability may be compromised due to the fact that the matrix can constrain the in-plane rotation of the serpentine. Comparison between the analytical solutions for freestanding serpentines and the FEM solutions for matrix-embedded serpentines reveals that matrix constraint remains trivial until the matrix modulus approaches that of the serpentine ribbon.

Non-Linear Numerical Simulation of Coiling by Elastic Finite Strain Model

The coiling process under traction is considered, with an incoming residual stress profile (that can be sufficiently compressive to make the strip buckle): a flatness defect. This paper details a 3D non-linear numerical simulation taking into account the contact of the strip on itself, with a perfect contact law. The model relies on elastic behavior at finite strain because of large rotations. Even though the behavior is elastic, the yield Von Mises criterion is computed and gives information about flatness defects (plastic zones are approximated by zones where the yield stress is exceeded). Furthermore, the paper aims at very short computation times. The modeling strategy relies (for each time step) on two analytical sub-steps. Numerical minimization procedure is used in order apply weak boundary conditions. Results are discussed with respect to a comprehensive Finite Element simulation and good agreement is observed.

A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

A new weak boundary procedure for hyperbolic problems is presented. We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique. The new boundary procedure is applied near boundaries in an extended domain where data is known. We show how to raise the order of accuracy of the scheme, how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries. The new boundary procedure is cheap, easy to implement and suitable for all numerical methods, not only finite difference methods, that employ weak boundary conditions. Numerical results that corroborate the analysis are presented.

Changing the symmetry of a homogeneous instability with a change in temperature in a stationary shear flow of a nematic with weak boundary conditions in an electromagnetic field

In this work, a numerical study is made of the induced switching symmetry of a homogeneous instability by temperature in a stationary shear flow of a nematic liquid crystal under electromagnetic field with weak boundary conditions.