We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.
Viscous flows within an elastic structure apply stress on the solid-liquid interface. The stress-field created by the viscous flow can be utilized to counter stress created by external forces and thus may be applied as a tool for delaying the onset of structural failure. To illustrate this concept we study viscous flow within an elastic cylinder under compressive axial force. We obtain a closed-form expression showing an approximately linear relation between the critical buckling load and the liquid inlet pressure. Our results are validated by numerical computations. We discuss future research…
The complexity and unpredictability of postbuckling responses in even simple thin shells have raised great challenges to emerging technologies exploiting buckling transitions. Here we comprehensively survey the buckling landscapes to show the full complexity of the stable buckling states and the transition mechanisms between each of them. This is achieved by combining a simple and versatile triangulated lattice model for modelling the shell morphologies with efficient high-dimensional free-energy minimisation and transition path finding algorithms. We show how the simple free energy landscapes…
We present a combined theoretical and experimental study of the buckling of a thin film wrapped around a sphere under the action of capillary forces. A rigid sphere is coated with a wetting liquid, and then wrapped by a thin film into an initially cylindrical shape. The equilibrium of this cylindrical shape is governed by the antagonistic effects of elasticity and capillarity: elasticity tends to keep the film developable while capillarity tends to curve it in both directions so as to maximize the area of contact with the sphere. In the experiments, the contact area between the film and the sp…
The orientational and translational order of a thermotropic ferroelectric liquid crystal (2MBOCBC) imbibed in self-organized, parallel, cylindrical pores with radii of 10, 15, or 20 nm in anodic aluminium oxide monoliths (AAO) are explored by high-resolution linear and circular optical birefringence as well as neutron diffraction texture analysis. The results are compared to experiments on the bulk system. The native oxidic pore walls do not provide a stable smectogen wall anchoring. By contrast, a polymeric wall grafting enforcing planar molecular anchoring results in a thermal-history indepe…
A general framework to study the mechanical behaviour of a cylindrical silicon anode particle in a lithium ion battery as it undergoes lithiation is presented. The two-way coupling between stress and concentration of lithium in silicon, including the possibility of plastic deformation, is taken into account and two particular cases are considered. First, the cylindrical particle is assumed to be free of surface traction and second, the axial deformation of the cylinder is prevented. In both cases plastic stretches develop through the entire cylinder and not just near the surface as is commonly…
A cylindrical hydrogel tube, completely submerged in water, hydrates by swelling and filling its internal cavity. When it comes back into contact with air, it dehydrates: the tube thus expels the solvent through the walls, shrinking. This dehydration process causes a depression in the tube cavity, which can lead to circumferential buckling. Here we study the occurrence of such buckling using a continuous model that combines non-linear elasticity with Flory-Rehner theory, to take into account both the large deformations and the active behavior of the hydrogel. In quasi-static approximation, we …
School of Integrated Design Engineering, Graduate School of Science and Technology, Keio University（庆应义塾大学理工学研究科综合设计工程学院）；Research Organization of Science and Technology, Ritsumeikan University（立命馆大学科学技术研究院）；Department of Mechanical Engineering, Faculty of Science and Technology, Keio University（庆应义塾大学理工学部机械工学科）
Euler's celebrated buckling formula gives the critical load $N$ for the buckling of a slender cylindrical column with radius $B$ and length $L$ as \[ N / (π^3 B^2) = (E/4)(B/L)^2, \] where $E$ is Young's modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness $(B/L)$ is an infinitesimal quantity. Here we ask the following question: What is the first nonlinear correction in the right hand-side of this equation when terms up to $(B/L)^4$ are kept? To answer this question, we specialize the exact solution of incremental non-linear…
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 pushed in the other direction, the bending direction can suddenly reverse. This instability is called snap-through buckling and is one of the elementary shape transitions in a prestressed thin structure. Combining experiments and theory, we study snap-buckling of an elastic strip with one end hinged and the other end clamped. These asymmetric boundary constr…
Nematic elastomers are programmable soft materials that display large, reversible and predictable deformation under an external stimulus such as a change in temperature or light. While much of the work in the field has focused on actuation from flat sheets, recent advances in 3D printing and other methods of directed synthesis have motivated the study of actuation of curved shells. Snap-through buckling has been a topic of particular interest. In this work, we present theoretical calculations to motivate another mode of actuation that combines programmable soft materials as well as instabiliti…
Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as uniaxially compressed soft-film/stiff-substrate systems. This can be explained by curvature effects. To investigate pattern transitions on a curved surface, we study a soft shell sliding on a rigid cylinder by experiments, computations and theoretical analyses. We reveal a novel post-buckling phenomenon involving multiple successive bifurcations: smooth-wrinkle-ridge-sagging transitions. The shell initially buckles into periodic axisymmetric wrinkles at the thre…
In this paper, we presented an experimental and theoretical analysis of the formation of the contact between a smooth elastomer lens and an elastomer substrate micropatterned with hexagonal arrays of cylindrical pillars. We show using a JKR model coupled with a full description of the deformation of the substrate between the pillars that the transition between the top to the full contact is obtain when the normal load is increased above a well predicted threshold. We have also shown that above the onset of full contact, the evolution of the area of full contact was obeying a simple scaling.
The design of compliant mechanisms is crucial in several technologies and relies on the availability of solutions for nonlinear structural problems. One of these solutions is given and experimentally validated in the present article for a compliant mechanism moving along a smooth curved profile. In particular, a deformable elastic rod is held by two clamps, one at each end. The first clamp is constrained to slide without friction along a curved profile, while the second clamp moves in a straight line transmitting its motion through the elastic rod to the first clamp. For this system it is show…
Rolling, sliding and trapping of driven particles in square obstacle lattices
Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC)（凝聚态物理中心（IFIMAC））；Instituto Nicolás Cabrera（尼古拉斯·卡布雷拉研究所）；Massachusetts Institute of Technology（麻省理工学院）
Volumetric expansion of silicon anode particles in a lithium-ion battery during charging may lead to the generation of undesirable internal stresses. For a cylindrical particle such growth may also lead to failure by buckling if the expansion is constrained in the axial direction due to other particles or supporting structures. To mitigate this problem, the possibility of reducing axial growth is investigated theoretically by studying simple modifications of the solid cylinder geometry. First, an annular cylinder is considered with lithiation either from the inside or from the outside. In both…
We study the rolling and sliding motion of droplets on a corrugated substrate by Molecular Dynamics simulations. Droplets are driven by an external body force (gravity) and we investigate the velocity profile and dissipation mechanisms in the steady state. The cylindrical geometry allows us to consider a large range of droplet sizes. The velocity of small droplets with a large contact angle is dominated by the friction at the substrate and the velocity of the center of mass scales like the square root of the droplet size. For large droplets or small contact angles, however, viscous dissipation…
We study the effect of film density on the uniaxial compression of thin elastic films at a liquid--fluid interface. Using a combination of experiments and theory, we show that dense films first wrinkle and then fold as the compression is increased, similarly to what has been reported when the film density is neglected. However, we highlight the changes in the shape of the fold induced by the film's own weight and extend the model of Diamant and Witten [Phys.Rev.Lett. 2011, 107, 164302, arXiv:1107.5505] to understand these changes. In particular, we suggest that it is the weight of the film tha…
