The Liquid Blister Test

We consider a thin elastic sheet adhering to a stiff substrate by means of the surface tension of a thin liquid layer. Debonding is initiated by imposing a vertical displacement at the centre of the sheet and leads to the formation of a delaminated region, or `blister'. This experiment reveals that the perimeter of the blister takes one of three different forms depending on the vertical displacement imposed. As this displacement is increased, we observe first circular, then undulating and finally triangular blisters. We obtain theoretical predictions for the observed features of each of these three families of blisters. The theory is built upon the F\"{o}ppl-von K\'{a}rm\'{a}n equations for thin elastic plates and accounts for the surface energy of the liquid. We find good quantitative agreement between our theoretical predictions and experimental results, demonstrating that all three families are governed by different balances between elastic and capillary forces. Our results may bear on micrometric tapered devices and other systems where elastic and adhesive forces are in competition.Comment: 23 pages, 11 figs approx published versio

Wrinkling of pressurized elastic shells

We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We present scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells

Indentation of ellipsoidal and cylindrical elastic shells

Thin shells are found in nature at scales ranging from viruses to hens’ eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus et al. [Phys. Rev. Lett. (submitted)] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells

The indentation of pressurized elastic shells: From polymeric capsules to yeast cells

Pressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of baker’s yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium

Buckling of swelling gels

The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel. When the structure is immersed in water, the soft gel swells and bends out of plane leading to a wavy periodic pattern which wavelength is measured. The linear stability of the flat state is studied in the framework of linear elasticity using the equations for thin plates. The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment

Measuring order in the isotropic packing of elastic rods

The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic two-dimensional confinement of a rod by a central force. We seek to measure how ordered is a folded configuration and we identify two key quantities. A geometrical characterization is given by the number of superposed layers in the configuration. Using temporal modulations of the confining force, we probe the mechanical properties of the configuration and we define and measure its effective compressibility. These two quantities may be used to build a statistical framework for packed elastic systems.Comment: 4 pages, 5 figure

Rescaling the dynamics of evaporating drops

The dynamics of evaporation of wetting droplets has been investigated experimentally in an extended range of drop sizes, in order to provide trends relevant for a theoretical analysis. A model is proposed, which generalises Tanner's law, allowing us to smooth out the singularities both in dissipation and in evaporative flux at the moving contact line. A qualitative agreement is obtained, which represents a first step towards the solution of a very old, complex problem

Slenderness Ratio and Influencing Parameters on the NL Behaviour of RC Shear Wall

Shear walls are very efficient structural elements to resist lateral seismic disturbance. Despite the aforementioned seismic performance, recent investigations report that they have suffered from significant structural damage after recent seismic activity, even for those complying with seismic provisions. These deficiencies in resistance and deformation capacities need to be explored. This study considers the influence of plastic length Lp, concrete compressive strength f_c28, longitudinal reinforcement ratio ρl, transverse reinforcement ratio ρsh, reduced axial load ν, confinement zone depth CS and focusing on the geometric slenderness λ. The parametric study has been conducted through NL pushover analysis using Peform3D software. The chosen coupled shear-flexure fiber macro model was calibrated with well-known cyclic experimental specimens. The paper points out the discrepancy between the two well-known codes EC8 and ASCE/SEI 41-13. In fact, the value of the slenderness ratio (λ) that trigger the beginning of a purely flexural behaviour recommended by EC8 (λ>2) is very different from the value of the ASCE/SEI 41-13 (λ>3) without accounting for the effect of the reduced axial force. Finally, it was found that RCW capacities are very sensitive to f_c28, ν, ρl, Lp and less sensitive to ρsh and CS. However, (λ) is the most decisive factor affecting the NL wall response. A new limit of slenderness and appropriate deformations of rotations are recommended to provide an immediate help to designers and an assistance to those involved with drafting codes. Doi: 10.28991/cej-2021-03091777 Full Text: PD

Are there waves in elastic wave turbulence ?

An thin elastic steel plate is excited with a vibrator and its local velocity displays a turbulent-like Fourier spectrum. This system is believed to develop elastic wave turbulence. We analyze here the motion of the plate with a two-point measurement in order to check, in our real system, a few hypotheses required for the Zakharov theory of weak turbulence to apply. We show that the motion of the plate is indeed a superposition of bending waves following the theoretical dispersion relation of the linear wave equation. The nonlinearities seem to efficiently break the coherence of the waves so that no modal structure is observed. Several hypotheses of the weak turbulence theory seem to be verified, but nevertheless the theoretical predictions for the wave spectrum are not verified experimentally.Comment: published in Physical Review Letters volume 100, 234505 (2008) http://link.aps.org/abstract/PRL/v100/e234505 minor modification

A comparative study of crumpling and folding of thin sheets

Crumpling and folding of paper are at rst sight very di erent ways of con ning thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly ine cient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than 6 or 7 times. Here we show that the sti ness that builds up in the two processes is of the same nature, and therefore simple folding models allow to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We nd that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio.Comment: 5 page