Localization of deformation in thin shells under indentation

Nasto, Alice; Ajdari, Amin; Lazarus, A. J.; Vaziri, Ashkan; Reis, Pedro

doi:10.1039/c3sm50279a

Cited by 53 publications

(63 citation statements)

References 49 publications

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“…4A). Upon indentation, for an uncreased shell (R s = 35 mm, α = 0) we observe a monotonically increasing load response similar to previous studies (1,38,45) (Fig. 4B).…”

Section: General Design Principlesupporting

confidence: 72%

“…Whereas the bending energy between the folded and unfolded states is infinite for isometric deformations, in any real material as the shell bends the energy will reach a scale where stretching = 0 > 0 < 0 Gaussian curvature, becomes favorable. As a result, our assumption that the shell does not stretch must have been flawed, and in-plane stresses must have developed near the fold similar to stress-focusing phenomena seen in other curved surfaces (1,(34)(35)(36)(37)(38)(39). Beyond this special stressed configuration, however, in-plane stresses are no longer necessary and the surface can, at least in principle, accommodate the folding through bending deformations alone.…”

Section: Geometrical Mechanics Of Folding a Shellmentioning

confidence: 99%

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Geometrically controlled snapping transitions in shells with curved creases

Bende

Evans

Innes-Gold

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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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 programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities.C urved shells are generally used to enhance structural stability (1-3), because the coupling between bending and stretching makes them energetically costly to deform. The consequences of this coupling are seen in both naturally occurring scenarios, such as intestinal villi and pollen grains (4, 5), and find use in man-made structures such as programmable metamaterials (6-9). When these shells have multistable configurations, the transition between them is opposed by geometrically enhanced rigidity resulting from the dominant stretching energy. Often, even for relatively small range of deformation, stretching leads to the high forces and rapid acceleration associated with a "snap-through" transition in many natural and man-made phenomena (10-17). For example, Venus flytraps (Dionaea muscipula) use this mechanism to generate a snapping motion to close their leaves (11), hummingbirds (Aves: Trochilidae) twist and rotate their curved beaks to catch insect prey (14), and engineered microlenses use a combination of bending and stretching energy to rapidly switch from convex to concave shapes to tune their optical properties (12). Despite the ability to engineer bistability and snapping transitions in a variety of systems by using prestress or material anisotropy (18-24), a general geometric design rule for creating a snap between stable states of arbitrary surfaces does not exist. This stands in stark contrast to the well-known rules and consequences fo...

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“…4A). Upon indentation, for an uncreased shell (R s = 35 mm, α = 0) we observe a monotonically increasing load response similar to previous studies (1,38,45) (Fig. 4B).…”

Section: General Design Principlesupporting

confidence: 72%

Section: Geometrical Mechanics Of Folding a Shellmentioning

confidence: 99%

Geometrically controlled snapping transitions in shells with curved creases

Bende

Evans

Innes-Gold

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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“…3.2 and 4.2, we study a Gaussian dimple and perform a parametric exploration of the influence of the defect shape on the buckling load. Both set of simulations assume axisymmetry to reduce the computational cost, since it has been shown that nonaxisymmetric bifurcations only take place far into the post-buckling regime [7,20,21].…”

Section: Simulation Methodsmentioning

confidence: 99%

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Marthelot

Jiménez

Lee

et al. 2017

Journal of Applied Mechanics

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We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry of the probe, we study the effect that the probe-induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predictions from the literature. Inspired by a nondestructive technique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells.

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“…Under point indentation, pressureless shells develop vertices [12][13][14][15][16] while pressurized shells wrinkle ( fig. 1b) [7].…”

Section: Comparison Of Floating Films To Pressurized Shellsmentioning

confidence: 99%

Wrinkling reveals a new isometry of pressurized elastic shells

Vella

Ebrahimi

Vaziri

et al. 2015

EPL

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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 instability. We show that rather than simply approaching the classical 'mirror-buckled' shape, the wrinkled shell approaches a new, universal shape that reflects a nontrivial type of isometry. For a given indentation depth, this "asymptotic isometry", which is only made possible by wrinkling, is reached in the doubly asymptotic limit of weak pressure and vanishing shell thickness.

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Localization of deformation in thin shells under indentation

Cited by 53 publications

References 49 publications

Geometrically controlled snapping transitions in shells with curved creases

Geometrically controlled snapping transitions in shells with curved creases

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Wrinkling reveals a new isometry of pressurized elastic shells

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