Related papers: Elastic energy for reflection-symmetric topologies
We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time $\lambda$ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a…
A model is derived for the viscoelastic response of glasses at isothermal uniaxial deformation with small strains. A glass is treated as an ensemble of relaxing units with various activation energies for rearrangement. With reference to the…
Permeative flows, known for the explanation of the anomalous viscosity (10^5 Poise) in cholesterics at low shear rates, are still under debate due to the difficulty of experiments. Here we use the Surface Force Balance, in which uniform…
Anti-plane shear deformations of a hexagonal quasi-crystal with multiple screw dislocations are considered. Using a variational formulation, the elastic equilibrium is characterized via limit of minimizers of a core-regularized energy…
In this paper, the two-dimensional pure bending of a hyperelastic substrate coated by a nematic liquid crystal elastomer (abbreviated as NLCE) is studied within the framework of nonlinear elasticity. The governing system, arising from the…
By analyzing elastic theory for nematic liquid crystals, we distinguish three regimes of elastic constants. In one regime, the Ericksen inequalities are satisfied, and the ground state of the director field is uniform. In a second regime,…
Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a…
We analyse a recent generalised free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform…
We analyze a model problem based on highly disparate elastic constants that we propose in order to understand corners and cusps that form on the boundary between the nematic and isotropic phases in a liquid crystal. For a bounded planar…
We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in…
We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nematic liquid crystal within a bounded domain in two or three…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of…
We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe extension of matching conditions by relaxing the vertex-rigidity assumption and the case in which concentrated mass may exists. This…
The capillary forces exerted by liquid drops and bubbles on a soft solid are directly measured using molecular dynamics simulations. The force on the solid by the liquid near the contact line is not oriented along the liquid vapor interface…
Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar…