Related papers: Straightening wrinkles
Entangled polymers are deformed by a strong shear flow. The shape of the polymer, called the form factor, is measured by small angle neutron scattering. However, the real-space molecular structure is not directly available from the…
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…
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…
A growing or compressed thin elastic sheet adhered to a rigid substrate can exhibit a buckling instability, forming an inward hump. Our study shows that the strip morphology depends on the delicate balance between the compression energy and…
Two model problems of an elastic wedge with an internal and edge crack are analyzed. The problem of an internal crack reduces to an order-4 vector Riemann-Hilbert problem whose matrix kernel entries are meromorphic functions and have…
Self-shaping of curved structures, especially those involving flexible thin layers, has attracted increasing attention because of their broad potential applications in e.g. nanoelectromechanical/micro-electromechanical systems (NEMS/MEMS),…
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 study the indentation of ultrathin elastic sheets clamped to the edge of a circular hole. This classical setup has received considerable attention lately, being used by various experimental groups as a probe to measure the surface…
Surface tension tends to minimize the area of interfaces between pieces of matter in different thermodynamic phases, be they in the solid or the liquid state. This can be relevant for the macroscopic shape of very soft solids, and lead to a…
When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking and forms a cylindrical arc, a phenomenon well known as Euler buckling. When this cylindrical section is…
The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic…
We investigate the relaxation of rectangular wrinkled thin films intrinsically containing an initial strain gradient. A preferential rolling direction, depending on wrinkle geometry and strain gradient, is theoretically predicted and…
A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical…
The wrinkle pattern exhibited upon stretching a rectangular sheet has attracted considerable interest in the "extreme mechanics" community. Nevertheless, key aspects of this notable phenomenon remain elusive. Specifically -- what is the…
A two dimensional amorphous material is modeled as an assembly of mesoscopic elemental pieces coupled together to form an elastically coherent structure. Plasticity is introduced as the existence of different minima in the energy landscape…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion…
It is known that beyond a critical speed, the straight contact line of a partially-wetting liquid destabilizes into a corner. In one of the earliest theoretical works exploring this phenomenon, [L. Limat and H. A. Stone, Europhys. Lett.…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
Twisted ribbons subjected to a tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. These shapes are intimately related to the instability of the natural, helicoidal symmetry…