相关论文: How paper folds: bending with local constraints

Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points,…

We present a microscopic variational theory for the free energy surface of a fast folding protein that allows folding kinetics to be resolved to the residue level using Debye-Waller factors as local order parameters. We apply the method to…

Any surface is completely characterized by a metric and a symmetric tensor satisfying the Gauss-Codazzi-Mainardi equations (GCM), which identifies the latter as its curvature. We demonstrate that physical questions relating to a surface…

The wrinkling of thin elastic objects provides a means of generating regular patterning at small scales in applications ranging from photovoltaics to microfluidic devices. Static wrinkle patterns are known to be governed by an energetic…

A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…

A remarkable property of flexible self-avoiding elastic surfaces (membranes) is that they remain flat at all temperatures, even in the absence of a bending rigidity or in the presence of active fluctuations. Here, we report numerical…

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally…

The response of paper to humidity variations is a complex multi-scale problem. The hygroscopic swelling of individual fibres and their interactions within the fibrous network govern the macroscopic response. At this scale, moisture induced…

Materials with J-shaped stress-strain behavior under uniaxial stretching, where strength increases as deformation progresses, have been developed through various materials designs. On the other hand, polymer materials that progressively…

When a body is exposed to external forces large local stresses may occur at the surface because of surface roughness. Surface stress concentration is important for many applications and in particular for fatigue due to pulsating external…

In two-dimensional Lennard-Jones glasses, mechanical probing reveals that local yield surfaces are dominated by regions with a positive second derivative of the yield stress with respect to the loading angle. Each feature corresponds to a…

Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…

Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…

Macroscopic friction coefficients observed in experiments are the result of various types of complex multiscale interactions between sliding surfaces. Therefore, there are several ways to modify them depending on the physical phenomena…

We characterise which simplicial surfaces can be folded onto a triangle. We define a notion of folding that incorporates the non-intersection-properties of real materials. All of the surfaces foldable onto a triangle admit a…

We study the pinning of a two-dimensional membrane to a patterned substrate within elastic theory both in the bending rigidity and in the strain dominated regimes. We find that both the in-plane strains and the bending rigidity can lead to…

Various adhesion mechanisms that have been understood in the field of synthetic adhesives are described and these are linked with situations relevant to fouling issues. The review mainly deals with mechanical aspects of adhesion phenomena,…

Subsurface projection has become indispensable in studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is sometimes called relative twisting. We give two…