Buckling-induced retraction of spherical shells: A study on the shape of aperture

Lin, Sen; Xie, Yi Min; Li, Qing; Huang, Xiaodong; Zhou, Shiwei

doi:10.1038/srep11309

Cited by 10 publications

(9 citation statements)

References 37 publications

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“…We then cooled the core/shell systems from different temperatures to the room temperature, which was used to mimic the increasing load of compressive strain in the film. The consistent delamination pattern of hexagonal dimples (reminiscent of the structure of a buckliball [Lin et al, 2015]) was observed on the spherical substrate in both experiments and parallel simulations, as shown in Figure 2. With increasing temperature drop amplitude, the number of hexagonal dimples grew progressively from only a few dimples to full coverage of the spherical surface, during which the increment of the delamination width of the hexagon's edge is small.…”

Section: Onset and Evolution Of Direct Delamination Patternssupporting

confidence: 73%

Curvature-controlled delamination patterns of thin films on spherical substrates

Zhu

Yuan

et al. 2021

iScience

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Summary Periodic delamination patterns in multilayer structures have exhibited extensive applications in microelectronics and optics devices. However, delamination behaviors of a closed thin shell on spherical substrates are still elusive. Herein, a unique instability mechanism of buckle delamination in a closed thin film weakly bonded to spherical substrates is studied by experiments, simulations, and theoretical analyses. The system of an Al film depositing on polystyrene spheres subjected to thermal mismatch strain is used for demonstration. Unlike traditional phenomena of wrinkling and wrinkle-induced delamination under increasing misfit strain, the weak adhesion between the core and shell results in a periodic pattern of delaminated hexagonal dimples that emerges directly from the smooth sphere configuration, before which no wrinkling occurs. Both substrate curvature and interfacial adhesion are revealed to control the dimple size and delamination width. These findings open a new venue for manifesting new controllable features for surface microfabrication.

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Section: Onset and Evolution Of Direct Delamination Patternssupporting

confidence: 73%

Curvature-controlled delamination patterns of thin films on spherical substrates

Zhu

Yuan

et al. 2021

iScience

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“…The aperture has a rounded-square shape in which the distance between the opposite vertices is 22. To obtain a buckliball with a large volume retraction ratio, a 2D pattern is first designed using a superformula, which can generate a variety of complex shapes 20 . Compared with circular apertures, the volume retraction ratio of a buckliball with rounded-square apertures can be improved by 8.65% 20 .…”

Section: Methodsmentioning

confidence: 99%

“…To obtain a buckliball with a large volume retraction ratio, a 2D pattern is first designed using a superformula, which can generate a variety of complex shapes 20 . Compared with circular apertures, the volume retraction ratio of a buckliball with rounded-square apertures can be improved by 8.65% 20 . Because the shape transformation is inherently reversible, an intuitive way to obtain the planar pattern of a 3D object is by unfolding it 21 .…”

Section: Methodsmentioning

confidence: 99%

A Kirigami Approach to Forming a Synthetic Buckliball

Lin

Xie

et al. 2016

Sci Rep

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The shape transformation of some biological systems inspires scientists to create sophisticated structures at the nano- and macro- scales. However, to be useful in engineering, the mechanics of governing such a spontaneous, parallel and large deformation must be well understood. In this study, a kirigami approach is used to fold a bilayer planar sheet featuring a specific pattern into a buckliball under a certain thermal stimulus. Importantly, this prescribed spherical object can retract into a much smaller sphere due to constructive buckling caused by radially inward displacement. By minimizing the potential strain energy, we obtain a critical temperature, below which the patterned sheet exhibits identical principal curvatures everywhere in the self-folding procedure and above which buckling occurs. The applicability of the theoretical analysis to the self-folding of sheets with a diversity of patterns is verified by the finite element method.

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“…Depending on the species, pollen changes its shape during desiccation in surprisingly different ways, from a regular infolding to a seemingly random, irregular fashion-even if the type of exine ornamentation and the aperture condition appear to be almost identical (2,5,26). Several theoretical studies have recently explored the role that apertures in pollen grains (25,27) or, more generally, local soft spots in elastic shells (28)(29)(30) play in their folding pathways. Studies of instabilities and buckling in thin shells (31)(32)(33)(34)(35) have shown that a perfectly homogeneous spherical shell exposed to uniform pressure or undergoing a change in volume will develop depressions in unpredictable positions due to the high symmetry of the problem (35,36).…”

Section: Biophysicsmentioning

confidence: 99%

Mechanical design of apertures and the infolding of pollen grain

Božič

Šiber

2020

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

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When pollen grains become exposed to the environment, they rapidly desiccate. To protect themselves until rehydration, the grains undergo characteristic infolding with the help of special structures in the grain wall—apertures—where the otherwise thick exine shell is absent or reduced in thickness. Recent theoretical studies have highlighted the importance of apertures for the elastic response and the folding of the grain. Experimental observations show that different pollen grains sharing the same number and type of apertures can nonetheless fold in quite diverse fashions. Using the thin-shell theory of elasticity, we show how both the absolute elastic properties of the pollen wall and the relative elastic differences between the exine wall and the apertures play an important role in determining pollen folding upon desiccation. Focusing primarily on colpate pollen, we delineate the regions of pollen elastic parameters where desiccation leads to a regular, complete closing of all apertures and thus to an infolding which protects the grain against water loss. Phase diagrams of pollen folding pathways indicate that an increase in the number of apertures leads to a reduction of the region of elastic parameters where the apertures close in a regular fashion. The infolding also depends on the details of the aperture shape and size, and our study explains how the features of the mechanical design of apertures influence the pollen folding patterns. Understanding the mechanical principles behind pollen folding pathways should also prove useful for the design of the elastic response of artificial inhomogeneous shells.

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Buckling-induced retraction of spherical shells: A study on the shape of aperture

Cited by 10 publications

References 37 publications

Curvature-controlled delamination patterns of thin films on spherical substrates

Curvature-controlled delamination patterns of thin films on spherical substrates

A Kirigami Approach to Forming a Synthetic Buckliball

Mechanical design of apertures and the infolding of pollen grain

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