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

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 develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we…

We study the behavior of thin elastic sheets that are bent and strained under the influence of weak, smooth confinement. We show that the emerging shapes exhibit the coexistence of two types of domains that differ in their characteristic…

Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…

The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wavevector set by the bending stiffness of the film and the weight of…

We study the dynamic coarsening of wrinkles in an elastic sheet that is compressed while lying on a thin layer of viscous liquid. When the ends of the sheet are instantaneously brought together by a small distance, viscous resistance…

This paper investigates the rigidity of bordered polyhedral surfaces. Using the variational principle, we show that bordered polyhedral surfaces are determined by boundary value and discrete curvatures on the interior edges. As a corollary,…

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…

The behavior of an elastic curve bound to a surface will reflect the geometry of its environment. This may occur in an obvious way: the curve may deform freely along directions tangent to the surface, but not along the surface normal.…

Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the…

A rectangular thin elastic sheet is deformed by forcing a contact between two points at the middle of its length. A transition to buckling with stress focusing is reported for the sheets sufficiently narrow with a critical width…

We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by…

Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…

Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…

When twisting a strip of paper or acetate under high longitudinal tension, one observes, at some critical load, a buckling of the strip into a regular triangular pattern. Very similar triangular facets have recently been observed in…

Consider a surface described by a Hamiltonian which depends only on the metric and extrinsic curvature induced on the surface. The metric and the curvature, along with the basis vectors which connect them to the embedding functions defining…

Thin sheets that are forced at their boundaries develop a variety of shapes aimed at minimising elastic energy by curving spontaneously in ways that break the symmetry of the sheet and the forcing. Characterising such buckling generally…

Single-mode deformations of two-dimensional materials, such as the Miura-ori zig-zag fold, are important to the design of deployable structures because of their robustness; these usually require careful pre-patterning of the material. Here…

In comparative and developmental neuroanatomy one encounters questions regarding the deformation of neural tissue under stress. The motivation of this note is an observation (Barbas {\it et al}) that at cortical folds or gyri, the layers of…

A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving…