相关论文: Universal wrinkling of supported elastic rings

Wrinkling of an inextensible elastic lining of an inner-lined tube under imposed pressure is considered. A simple equation modeling the elastic properties of the lining, the pressure, and the soft-substrate forces is derived. This equation…

We present a combined analytical approach and numerical study on the stability of a ring bound to an annular elastic substrate, which contains a circular cavity. The system is loaded by depressurizing the inner cavity. The ring is modeled…

We consider the point indentation of a pressurized, spherical elastic shell. Previously it was shown that such shells wrinkle once the indentation reaches a threshold value. Here, we study the behaviour of this system beyond the onset of…

The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring or tube could take subject to a uniform hydrostatic pressure are presented in an explicit analytic form. The…

Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal…

Buckling and barrelling instabilities in the uniaxial compressions of an elastic rectangle have been studied by many authors under lubricated end conditions. However, in practice it is very difficult to realize such conditions due to…

We investigate the elasticity of unsupported epithelial monolayer and we discover that unlike a thin solid plate, which wrinkles if geometrically incompatible with the underlying substrate, the epithelium may do so even in absence of the…

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,…

The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are demonstrated. A model based on small deflection thin shell theory, the equations of which are solved in…

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 investigate the wrinkling dynamics of a thin elastic sheet that is indented or compressed while floating on a viscous liquid. We show that the deformation speed controls the dynamics, leading to a wrinkle wavelength significantly smaller…

Snapping mechanisms are investigated for an elastic strip with ends imposed to move and rotate in time. Attacking the problem analytically via Euler's elastica and the second variation of the total potential energy, the number of stable…

We consider a disk-shaped thin elastic sheet bonded to a compliant sphere. (Our sheet can slip along the sphere; the bonding controls only its normal displacement.) If the bonding is stiff (but not too stiff), the geometry of the sphere…

Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…

Knitted fabrics exhibit high flexibility due to their periodic loop structures formed by bent yarns. Under compressive loading, they develop three-dimensional (3D) wrinkling patterns that reflect nonlinear interactions between yarn…

A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…

We study the peculiar wrinkling pattern of an elastic plate stamped into a spherical mold. We show that the wavelength of the wrinkles decreases with their amplitude, but reaches a maximum when the amplitude is of the order of the thickness…

Thin rigid sheets floating on a liquid substrate appear, for example, in coatings and surfactant monolayers. Upon uniaxial compression the sheet undergoes transitions from a compressed flat state to a periodic wrinkled pattern to a…

In [Pal et al., arXiv:2206.03552], the authors discuss how an unsupported flat annulus contracted at its inner boundary by a factor $\Delta$, buckles into a radial wrinkling pattern that is fully isometric and tension-free. What selects the…

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions.…