Related papers: How periodic surfaces bend without stretching
Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither…
We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…
We consider periodic arrangements of metal nanostructures and study the effect of periodicity on the localised surface plasmon resonance of the structures within an electrostatic eigenmode approximation. We show that within this limit, the…
The elastic response of the crystalline sheet to the stretching deformation in the form of wrinkles has been extensively investigated. In this work, we extend this fundamental scientific question to the plastic regime by exploring the…
To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we…
In this letter, we investigate the geometrically tailorable elasticity in the twisting behavior of biomimetic scale-covered slender soft substrate. Motivated by our qualitative experiments showing a significant torsional rigidity increase,…
A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the…
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…
The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model.…
In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal…
We study the stability of filaments in equilibrium between gravity and internal as well as external pressure using the grid based AMR-code RAMSES. A homogeneous, straight cylinder below a critical line mass is marginally stable. However, if…
We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a…
Various aspects of axion electrodynamics in the presence of a homogeneous and isotropic dielectric medium are discussed. 1. We consider first the "antenna-like" property of a planar dielectric surface in axion electrodynamics, elaborating…
Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…
The mechanical properties of tissues play an essential role for all tissue properties such as cell division, and differentiation or morphogenesis. Here, we study theoretically the rheology of 2-dimensional epithelial tissues described by a…
Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
We consider an ideal gas of infinitely rigid rods near a perfectly repulsive wall, and show that the interfacial tension of a surface with rods on one side is lower when the surface bends towards the rods. Surprisingly we find that rods on…
Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical…