Related papers: Nonrigidity of flat ribbons
We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state,…
Topology is an important determinant of the behavior of a great number of condensed-matter systems, but until recently has played a minor role in elasticity. We develop a theory for the deformations of a class of twisted non-Euclidean…
Since graphene nanoribbons are thin and flimsy, they need support. Support gives firm ground for applications, and adhesion holds ribbons flat, although not necessarily straight: ribbons with high aspect ratio are prone to bend. The effects…
The mechanical response of graphene nano-ribbon under tensile loading has been investigated using atomistic simulation. Lattice symmetry dependence of elastic properties are found, which fits prediction from Cauchy-Born rule well.…
We investigate the quantum mechanics of a single particle constrained to move along an arbitrary smooth reference curve by a confinement that is allowed to vary along the waveguide. The Schr\"odinger equation is evaluated in the adapted…
Atomistic simulations are used to study the bending of rectangular graphene nano ribbons subjected to axial stress both for free boundary and supported boundary conditions. The shape of the deformations of the buckled graphene nano ribbons,…
We prove that ribbons, i.e. double structures associated with a line bundle $\SE$ over its reduced support, a smooth irreducible projective curve of arbitrary genus, are smoothable if their arithmetic genus is greater than or equal to $3 $…
Graphene nanoribbons are prone to in-plane bending even when supported on flat substrates. However, the amount of bending that ribbons can stably withstand remains poorly known. Here, by using molecular dynamics simulations, we study the…
We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive…
We study the effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed…
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative $L^2$-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic…
One cannot pull an open, curved string along itself. This fact is clearly reflected in the unwrapping motion of a string or chain as it is dragged around an object, and implies strong consequences for slender structures in passive…
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…
Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example when a ribbon has half a twist and is…
Change of the bonding environment at the free edges of graphene monolayer leads to excess edge energy and edge force, depending on the edge morphology (zigzag or armchair). By using a reactive empirical bond-order potential and atomistic…
The low-Reynolds number hydrodynamics of slender ribbons is accurately captured by slender-ribbon theory, an asymptotic solution to the Stokes equation which assumes that the three length scales characterising the ribbons are well…
A ribbon is a non-reduced curve modelled on the first infinitesimal neighbourhood of a smooth curve in a surface. This paper is devoted to describe some properties of coherent sheaves on such a curve and their Simpson moduli space. In…
The electronic and transport properties of an extended linear defect embedded in a zigzag nanoribbon of realistic width are studied, within a tight binding model approach. Our results suggest that such defect profoundly modify the…
We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full $\Gamma$-convergence result. The…