arXiv subjects

Oz Oshri

Publications and source records attributed to Oz Oshri.

5 recordsLinked to original sources

arXiv2023

Fluttering-induced flow in a closed chamber

We study the emergence of fluid flow in a closed chamber that is driven by dynamical deformations of an elastic sheet. The sheet is compressed between the sidewalls of the chamber and partitions it into two separate parts, each of which is initially filled with an inviscid fluid. When fluid exchange is allowed between the two compartments of the chamber, the sheet becomes unstable, and its motion displaces the fluid from rest. We derive an analytical model that accounts for the coupled, two-way, fluid-sheet interaction. We show that the system depends on four dimensionless parameters: the normalized excess length of the sheet compared to the lateral dimension of the chamber, $Δ$; the normalized vertical dimension of the chamber; the normalized initial volume difference between the two parts of the chamber, $v_{\text{du}}(0)$; and the structure-to-fluid mass ratio, $λ$. We investigate the dynamics at the early times of the system's evolution and then at moderate times. We obtain the growth rates and the frequency of vibrations around the second and the first buckling modes, respectively. Analytical solutions are derived for these linear stability characteristics within the limit of the small-amplitude approximation. At moderate times, we investigate how the sheet escapes from the second mode. Given the chamber's dimensions, we show that the initial energy of the sheet is mostly converted into hydrodynamic energy of the fluid if $λ\ll 1$, and into kinetic energy of the sheet if $λ\gg 1$. In both cases most of the initial energy is released at time $ t_{\text{p}}\simeq \ln[c Δ^{1/2}/v_{\text{du}}(0)]/σ$, where $σ$ is the growth rate and $c$ is a constant.

physics.flu-dyn↗

arXiv2017

Pattern transitions in a compressible floating elastic sheet

Thin rigid sheets floating on a liquid substrate appear, for example, in coatings and surfactant monolayers. Upon uniaxial compression the sheet undergoes transitions from a compressed flat state to a periodic wrinkled pattern to a localized folded pattern. The stability of these states is determined by the in-plane elasticity of the sheet, its bending rigidity, and the hydrostatics of the underlying liquid. Wrinkles and folds, and the wrinkle-to-fold transition, were previously studied for incompressible sheets. In the present work we extend the theory to include finite compressibility. We analyze the details of the flat-to-wrinkle transition, the effects of compressibility on wrinkling and folding, and the compression field associated with the pattern formation. The state diagram of the floating sheet including all three states is presented.

cond-mat.soft↗

arXiv2017

Strain tensor selection and the elastic theory of incompatible thin sheets

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.

cond-mat.soft↗

arXiv2016

Properties of compressible elastica from relativistic analogy

Kirchhoff's kinetic analogy relates the deformation of an incompressible elastic rod to the classical dynamics of rigid body rotation. We extend the analogy to compressible filaments and find that the extension is similar to the introduction of relativistic effects into the dynamical system. The extended analogy reveals a surprising symmetry in the deformations of compressible elastica. In addition, we use known results for the buckling of compressible elastica to derive the explicit solution for the motion of a relativistic nonlinear pendulum. We discuss cases where the extended Kirchhoff analogy may be useful for the study of other soft matter systems.

cond-mat.soft↗

arXiv2015

Wrinkles and folds in a fluid-supported sheet of finite size

A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength $λ$. As the confinement increases, the deformation energy is progressively localized into a single narrow fold. An exact solution for the deformation of an infinite sheet was previously found, indicating that wrinkles in an infinite sheet are unstable against localization for arbitrarily small confinement. We present an extension of the theory to sheets of finite length $L$, accounting for the experimentally observed wrinkle-to-fold transition. We derive an exact solution for the periodic deformation in the wrinkled state, and an approximate solution for the localized, folded state. We show that a second-order transition between these two states occurs at a critical confinement $Δ_F=λ^2/L$.

cond-mat.soft↗