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

Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on…

In our common experience, crumpling a sheet requires external compressive force and leads to a random network of folds. However, thin sheets have been theoretically predicted to spontaneously transition from a flat to a crumpled state…

In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven…

When a thin sheet is crushed into a small three-dimensional volume, it invariably forms a structure with a low volume fraction but high resistance to further compression. Being a far-from-equilibrium process, forced crumpling is not…

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…

A method is given for evaluating electromagnetic scattering by an irregular surface with spatially-varying impedance. This uses an operator expansion with respect to impedance variation and allows examination of its effects and the…

Localization of plastic strain induced by softening can be objectively described by a regularized plasticity model that postulates a dependence of the current yield stress on a nonlocal softening variable defined by a differential…

Buckling in compression is the archetype of elastic instability: when compressed along its longest dimension, a thin structure such as a playing card will buckle out-of-plane accommodating the imposed compression without a significant…

Periodic wrinkling of a rigid capping layer on a deformable substrate provides a useful method for templating surface topography for a variety of novel applications. Many experiments have studied wrinkle formation during the compression of…

Soft elastic sheets resting on rigid surfaces develop wrinkles, rucks, and folds due to the combined influence of elasticity, gravity, and contact interactions. Despite their ubiquity, the principles governing their morphology and…

We discuss a 1D variational problem modeling an elastic sheet on water, lifted at one end. Its terms include the membrane and bending energy of the sheet as well as terms due to gravity and surface tension. By studying a suitable…

The phenomenon of crumpling is common in our daily life and nature. It exhibits many interesting properties, such as ultra-tough resistance to pressure with less than 30$\%$ of volume density, power-law relation for pressure vs density, and…

Thin surfaces are ubiquitous in nature, from leaves to cell membranes, and in technology, from paper to corrugated containers. Structural thinness imbues them with flexibility, the ability to easily bend under light loads, even as their…

In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…

A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…

We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical and experimental methods. Such sheets occur in packaging, surgery and nanotechnology. We…

This paper investigates the motion of falling leaves through modeling using papers and the corresponding data collected from more than four thousands experiments. Two series of experiments were designed in order to study the relationship…

Recently, topography change by illumination of pre-stretched, flat sheets covered in ink of optical density varying in-plane has been demonstrated by Mailen\textit{ et al}, Smart Materials and Structures, 2019. They reduce an analysis of…

Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric…