Related papers: Finite curved creases in infinite isometric sheets
Geometric rectification of images of distorted documents finds wide applications in document digitization and Optical Character Recognition (OCR). Although smoothly curved deformations have been widely investigated by many works, the most…
The preference of thin flat sheets to bend rather than stretch, combined with results from Geometry, mean that changes in a thin sheet's Gaussian curvature are prohibitively expensive. As a result, an imposed curvature in one principal…
We investigate the formation dynamics of plastic creases in thin elasto-plastic sheets. In contrast to the commonly accepted description of crumpled thin sheets, which asserts that creases form only by elastic interaction between two…
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…
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…
Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains, to wrinkled membranes and…
We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate non-zero Gaussian curvature up to size scales that ultimately vanish with their elastic…
In this paper we consider developable surfaces which are isometric to planar domains and which are piecewise differentiable, exhibiting folds along curves. The paper revolves around the longstanding problem of existence of the so-called…
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…
In geometrically frustrated assemblies local inter-subunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here, we use theory and coarse-grained simulation to study a…
An elastic membrane that is forced to reside in a container smaller than its natural size will deform and, upon further volume reduction, eventually crumple. The crumpled state is characterized by the localization of energy in a complex…
It is well-known that a thin sheet held in a rigid circular clamp has a larger flexural strength than when it is flat. Here, we report that the flexural strength of curved sheets is further increased with a softening of the clamping…
We present two-dimensional simulations of finite, self-gravitating gaseous sheets. Unlike the case of infinite sheets, such configurations do not constitute equilibrium states but instead are subject to global collapse unless countered by…
Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self-contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where…
In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lam\'{e} system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial…
We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the transition zone in…
We study the deformation of a liquid interface with arbitrary principal curvatures by a flat circular sheet. Working first at small slopes, we determine the shape of the sheet analytically in the membrane limit, where the sheet is…
In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing…
In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container. We show that this feature is independent of thickness of the sheet,…
We investigate the dissipative mechanisms exhibited by creased material sheets when subjected to mechanical loading, which comes in the form of plasticity and relaxation phenomena within the creases. After demonstrating that plasticity…