相关论文: The Geometry of Crumpled Paper

A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles -- in which resides the elastic energy -- put in a confining potential. Many independent equilibrium configurations are…

Hand crumpled paper balls involve intricate structure with a network of creases and vertices, yet show simple scaling properties, which suggests self-similarity of the structure. We investigate the internal structure of crumpled papers by…

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.…

Crumpled thin sheets are complex fractal structures whose physical properties are influenced by a hierarchy of ridges. In this Letter, we report experiments that measure the stress-strain relation and show the coexistence of phases in the…

The network formed by ridges in a straightened sheet of crumpled paper is studied using a laser profilometer. Square sheets of paper were crumpled into balls, unfolded and their height profile measured. From these profiles the imposed…

We study the roughness of randomly crumpled elastic sheets. Based on analytical and numerical calculations, we find that they are self affine with a roughness exponent equal to one. Such crumpling occurs {\it e.g.\/} when wet paper dries.…

We study numerically the stress distribution on the interface between two thick elastic media bounded by interfaces that include spatially correlated asperities. The interface roughness is described using the self-affine topography that is…

When a thin elastic sheet is confined to a region much smaller than its size the morphology of the resulting crumpled membrane is a network of straight ridges or folds that meet at sharp vertices. A virial theorem predicts the ratio of the…

A three-dimensional X-ray tomography is performed to investigate the internal structure and its evolution of a crumpled aluminum foil. The upper and lower bounds of the internal geometric fractal dimension are determined, which increase…

Crumpling and folding of paper are at rst sight very di erent ways of con ning thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities…

When a thin elastic sheet crumples, the elastic energy condenses into a network of folding lines and point vertices. These folds and vertices have elastic energy densities much greater than the surrounding areas, and most of the work…

A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper…

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…

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…

Conforming materials to rigid substrates with Gaussian curvature --- positive for spheres and negative for saddles --- has proven a versatile tool to guide the self-assembly of defects such as scars, pleats, folds, blisters, and liquid…

Blisters are commonly observed when an adhesive sheet is carelessly deposited on a plate. Although such blisters are usually not desired for practical applications, we show through model experiments on angular blisters how material…

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 report an experimental study of the development of orientational order in a crumpled sheet, with a particular focus on the role played by the geometry of confinement. Our experiments are performed on elastomeric sheets immersed in a…

Large deformations of thin elastic plates and shells present a formidable problem in continuum mechanics which is generally intractable except by numerical methods. Conventional approaches break down in the limit of small plate thickness…

Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…