Snap buckling of a confined thin elastic sheet

Napoli, Gaetano; Turzi, Stefano

doi:10.1098/rspa.2015.0444

Cited by 23 publications

(25 citation statements)

References 27 publications

(44 reference statements)

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“…Hence, with regards to the local stability of solutions, we immediately deduce that the upper-branch of the buckled solution is an energy maximum, while the remaining dashed lines are metastable states. A more rigorous analysis of the local stability confirms these predictions and has been carried out in a closely related problem with a similar bifurcation diagram in Ref [8].…”

Section: Numerical Results and Energy Landscapesupporting

confidence: 67%

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The delamination of a growing elastic sheet with adhesion

Napoli

Turzi

2017

Meccanica

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We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth causes residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at which the instability occurs. We show that the critical threshold scales with a single dimensionless parameter that comprises information from the geometry of the sheet, the mechanical parameters of material and the adhesive features of the substrate

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Section: Numerical Results and Energy Landscapesupporting

confidence: 67%

“…The critical threshold depends on the balance between the elastic and adhesive energies of the substrate and the bending energy of the film. The birth of a blister related to the growth or compression of a sheet inside a curved cylinder has been analysed in a previous paper [8]. Lee and al.…”

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confidence: 99%

The delamination of a growing elastic sheet with adhesion

Napoli

Turzi

2017

Meccanica

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“…However, we also note that immediately after the buckled solution appears, it has a slightly higher energy than the unbuckled state and thus is only metastable. (We note that a cusped energy curve with a small portion of the buckled state that is metastable was also observed in a related study [20].) Nevertheless, the length of this metastable branch decreases for decreasing SL ∞ , and as ∆L increases, the energy of this buckled state is considerably lower than that of the unbuckled, purely compressed state.…”

Section: Multiple Statessupporting

confidence: 80%

“…We note that in other problems where non-zero extensibility has been found to play a role, the relevant stretchability parameter has been determined purely from the geometry of the system. For example, the growth of a rod confined within a circular tube is controlled by the ratio of the rod thickness to the cylinder radius [20], while the buckling, snap-through and 'ringing' oscillation of beams and arches depends on the ratio of thickness to beam length [18,19]. In contrast, for the birth of a ruck in a rug, the relevant stretchability is S = t 2 /(12 2 g ).…”

Section: Resultsmentioning

confidence: 99%

The role of extensibility in the birth of a ruck in a rug

Lee

Gouellec

Vella

2015

Extreme Mechanics Letters

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Everyday experience suggests that a 'ruck' forms when the two ends of a heavy carpet or rug are brought closer together. Classical analysis, however, shows that the horizontal compressive force needed to create such a ruck should be infinite. We show that this apparent paradox is due to the assumption of inextensibility of the rug. By accounting for a finite extensibility, we show that rucks appear with a finite, non-zero end-shortening and confirm our theoretical results with simple experiments. Finally, we note that the appropriate measure of extensibility, the stretchability, is in this case not determined purely by geometry, but incorporates the mechanics of the sheet.

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“…Thus, from here on, we refer to the first blister solution as the one that is physically accessible. We note that this subtle, nonmonotonic behavior of the pressure-displacement relation has already been observed in other closely related systems [34,58,59].…”

Section: A Energy and Pressure-displacement Relationsupporting

confidence: 78%

Delamination of a thin sheet from a soft adhesive Winkler substrate

et al. 2018

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A uniaxially compressed thin elastic sheet that is resting on a soft adhesive substrate can form a blister, which is a small delaminated region, if the adhesion energy is sufficiently weak. To analyze the equilibrium behavior of this system, we model the substrate as a Winkler or fluid foundation. We develop a complete set of equations for the profile of the sheet at different applied pressures. We show that at the edge of delamination, the height of the sheet is equal to sqrt[2]ℓ_{c}, where ℓ_{c} is the capillary length. We then derive an approximate solution to these equations and utilize them for two applications. First, we determine the phase diagram of the system by analyzing possible transitions from the flat and wrinkled to delaminated states of the sheet. Second, we show that our solution for a blister on a soft foundation converges to the known solution for a blister on a rigid substrate that assumed a discontinuous bending moment at the blister edges. This continuous convergence into a discontinuous state marks the formation of a boundary layer around the point of delamination. The width of this layer relative to the extent length of the blister, ℓ, scales as w/ℓ∼(ℓ_{c}/ℓ_{ec})^{1/2}, where ℓ_{ec} is the elastocapillary length scale. Notably, our findings can provide guidelines for utilizing compression to remove thin biofilms from surfaces and thereby prevent the fouling of the system.

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Snap buckling of a confined thin elastic sheet

Cited by 23 publications

References 27 publications

The delamination of a growing elastic sheet with adhesion

The delamination of a growing elastic sheet with adhesion

The role of extensibility in the birth of a ruck in a rug

Delamination of a thin sheet from a soft adhesive Winkler substrate

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