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Charlotte Py has investigated elasto-capillarity, including how surface tension deforms an elastic sheet. She is the first author of the 2007 study introducing capillary origami: spontaneous wrapping of a liquid droplet by a flexible sheet.^[ref]

The experiment used thin polydimethylsiloxane sheets cut into different shapes. As water evaporated, surface tension progressively curved the sheet around the diminishing droplet. Square and triangular cuts followed different folding sequences, while sufficiently small or stiff sheets reopened rather than completely enclosing the liquid. This connected an accessible observation with a competition between surface energy and elastic bending.^[ref]

A complementary loop experiment measured the elastocapillary length: a wetting meniscus held a long strip in a loop whose shape could be compared with an elastic calculation. The resulting length scale helped organize the threshold for enclosure across sheet thicknesses and geometries.^[ref]

The sheet elastocapillary energy ratio compares capillary and bending energy scales for an elastic sheet:Here $L$ is a lateral size, $\gamma$ is surface tension, $B$ is plate bending stiffness and ${\ell }_{\mathrm{ec}}$ is the elastocapillary length. The ratio is a dimensionless quantity: $\gamma L^2$ and $B$ both have units of energy.

The estimate assumes bending through an angle of order one over size $L$. Then curvature scales as $1/L$ and integrating the bending energy density over area $L^2$ gives a scale $B$. A comparable change in interfacial area gives a surface energy scale $\gamma L^2$. The same balance underlies the capillary origami study's definition of elastocapillary length.^[ref]

For an original calculation, take $B=2\times 10^{-8}\mathrm{N}\mathrm{m}$, $\gamma =0.05N/m$ and $L=1\mathrm{mm}$. Then $\eta =2.5$. Doubling $L$ alone raises it to 10. Halving thickness at fixed $L$, Young's modulus and Poisson's ratio divides $B$ by eight and raises $\eta$ to 20.

Changing all dimensions gives another trend. Write $s=L/L_0$ and keep material properties and surface tension fixed. At fixed thickness, $\eta /{\eta }_0=s^2$; at fixed aspect ratio $h/L$, $B/B_0=s^3$ and $\eta /{\eta }_0=s^{-1}$. Thus halving $L$ alone gives one quarter of the initial ratio, while halving both $L$ and $h$ doubles it.

A larger ratio makes capillary energy more competitive with bending, but does not establish complete closure. Actual wetting, contact angle, droplet volume, contact-line pinning and accessible deformation paths also matter. The ratio compares scales rather than computing the full change in energy along a folding path.

The uniaxial sheet stretching stiffness is the coefficient relating axial force per unit width to axial engineering strain in a homogeneous thin elastic sheet under uniaxial stress with free lateral contraction. With Young's modulus $E$ and thickness $h$,Here $N=F/w$ for tensile force $F$ and sheet width $w$. Since Hooke's law gives $\sigma =E\epsilon$ and $F=\sigma wh$, division by $w$ gives the result. $Y_{2D}$ has units $N/m$, while $E$ has units $N/{\mathrm{m}}^2$.^[ref]

For an original example, choose $E=2\mathrm{GPa}$, $h=50\mu \mathrm{m}$, $w=10\mathrm{mm}$ and gauge length $L=50\mathrm{mm}$. Then $Y_{2D}=100000N/m$. At strain $\epsilon =0.001$, $N=100N/m$, $F=1\mathrm{N}$ and extension $\delta =\epsilon L=50\mu \mathrm{m}$. The specimen's axial stiffness is $F/\delta =Y_{2D}w/L=20000N/m$, which depends on its width and gauge length.

A tensile measurement can infer $Y_{2D}$ from the slope of $F/w$ against $\delta /L$. It needs known dimensions, reasonably uniform loading and freedom for lateral contraction; unloading tests elastic recovery. If lateral strain is instead constrained to zero while through-thickness stress remains zero, the plane stress equations give coefficient $Eh/(1-{\nu }^2)$, with $\nu$ Poisson's ratio.^[ref] The loading condition is part of the meaning of the reported stiffness.