Impact dynamics for a floating elastic membrane

Duchemin, Laurent; Vandenberghe, Nicolas

doi:10.1017/jfm.2014.471

Cited by 10 publications

(17 citation statements)

References 17 publications

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“…The scaling in (r/r i ) −3/2 agrees with the results in figure 7(b) and 8 and with the measurements presented in figure 6. It is also compatible with the self-similar scaling of equation (17): taking t = (r f /a) 3/2 in equation (19)…”

Section: Scaling For the Strainsupporting

confidence: 68%

“…The form (19) is valid on a large domain including r f but not near the impactor (r > ∼ r i ) as seen in figure 8. Looking for a generalization of equation (19), we postulate that the strains behave like s (r, t) = (V t/r i )E s (r/r i ) and θ (r, t) = (V t/r i )E θ (r/r i ).…”

Section: Scaling For the Strainmentioning

confidence: 94%

“…Looking for a generalization of equation (19), we postulate that the strains behave like s (r, t) = (V t/r i )E s (r/r i ) and θ (r, t) = (V t/r i )E θ (r/r i ). We recall that these time and space dependancies are compatible with the self-similarity observed experimentally, provided the function E s and E θ scale like equation (19) (11) and (7). The dashed line corresponds to the function β(r/ri) −3/2 , where β has been deduced from experimental measurements.…”

Section: Scaling For the Strainmentioning

confidence: 99%

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Impact on floating membranes

Vandenberghe

Duchemin

2016

Phys. Rev. E

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When impacted by a rigid object, a thin elastic membrane with negligible bending rigidity floating on a liquid pool deforms. Two axisymmetric waves radiating from the impact point propagate. In the first place, a longitudinal wave front -associated with in-plane deformation of the membrane and traveling at constant speed -separates an outward stress free domain with a stretched but flat domain. Then, in the stretched domain a dispersive transverse wave travels at a wave speed that depends on the local stretching rate. We study the dynamics of this fluid-body system and we show that the wave dynamics is similar to the capillary waves that propagate at a liquid-gas interface but with a surface tension coefficient that depends on impact speed. We emphasize the role of the stretching in the membrane in the wave dynamics but also in the development of a buckling instability that give rise to radial wrinkles.

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Section: Scaling For the Strainsupporting

confidence: 68%

Section: Scaling For the Strainmentioning

confidence: 94%

Section: Scaling For the Strainmentioning

confidence: 99%

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Impact on floating membranes

Vandenberghe

Duchemin

2016

Phys. Rev. E

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“…Previous work on dynamic impact-induced wrinkling has focused on situations in which the sheets are relatively extensible: Vermorel et al [22] studied a sheet with zero applied background stress impacted by a sphere, which shows the propagation of a longitudinal sound wave in the sheet followed by wrinkling. More recently, impact onto a floating sheet has been considered in two-dimensional [23] and axisymmetric [24] configurations. Again these experiments demonstrated that a tensile wave emanates from the point of impact and travels through the sheet at the speed of sound.…”

Section: Introductionmentioning

confidence: 99%

Impact on floating thin elastic sheets: A mathematical model

et al. 2020

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We investigate impact of a sphere onto a floating elastic sheet and the resulting formation and evolution of wrinkles in the sheet. Following impact, we observe a radially propagating wave, beyond which the sheet remains approximately planar but is decorated by a series of radial wrinkles whose wavelength grows in time. We develop a mathematical model to describe these phenomena by exploiting the asymptotic limit in which the bending stiffness is small compared to stresses in the sheet. The results of this analysis show that, at a time t after impact, the transverse wave is positioned a radial distance r ∼ t 1/2 from the impactor, in contrast to the classic r ∼ t 2/3 scaling observed for capillary-inertia ripples produced by dropping a stone into a pond. We describe the shape of this wave, starting from the simplest case of a point impactor and subsequently addressing a finite-radius spherical impactor. We show also that the coarsening of wrinkles in the flat portion of the sheet is controlled by the inertia of the underlying liquid: short-wavelength, small-amplitude wrinkles form at early times since they accommodate the imposed solid deformation without significantly displacing the underlying liquid. As time progresses, the liquid accelerates and the wrinkles grow larger and coarsen. We explain this coarsening quantitatively using numerical simulations and scaling arguments. arXiv:1811.11288v2 [cond-mat.soft] 21 Dec 2018 2

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“…Duchemin & Vandenberghe (2014) examined the dynamics due to impact of a rigid body on a thin elastic sheet laying over a liquid. Tulchinsky & Gat (2015) studied externally forced deformation of a saturated poroelastic medium laying on rough wet surface in the context of adhesion.…”

Section: Introductionmentioning

confidence: 99%

Transient dynamics of an elastic Hele-Shaw cell due to external forces with application to impact mitigation

Tulchinsky¹,

Gat²

2016

J. Fluid Mech.

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We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the flow-field via the lubrication approximation, and the plate deformation by the Kirchhoff-Love plate theory. We obtain a self-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed form expressions. We examine a uniform external pressure acting on the elastic plate over a finite region and during a finite time period, similar to the viscous-elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure, thus suggesting such configurations may be used for impact mitigation.

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Impact dynamics for a floating elastic membrane

Cited by 10 publications

References 17 publications

Impact on floating membranes

Impact on floating membranes

Impact on floating thin elastic sheets: A mathematical model

Transient dynamics of an elastic Hele-Shaw cell due to external forces with application to impact mitigation

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