Floating Carpets and the Delamination of Elastic Sheets

We investigate the deformation of a thin elastic sheet floating on a liquid surface and subject to a uniaxial compression. We show that at a critical compression the sheet delaminates from the liquid over a finite region forming a delamination “blister.” This blistering regime adds to the wrinkling and localized folding regimes that have been studied previously. The transition from wrinkled to blistered states occurs when delamination becomes energetically favorable compared with wrinkling. We determine the initial blister size and the evolution of blister size with continuing compression before verifying our theoretical results with experiments at a macroscopic scale.

Figure 1

Top: Schematic diagram of a sheet floating on the surface of a liquid and subject to a uniaxial compression $\Delta l$. The compression is such that the sheet delaminates from the liquid over a horizontal distance $b$ forming a delamination “blister.” Bottom: Experimental and theoretical profiles of a blistered sheet (thickness $h=1.6\mathrm{mm}$) for $\Delta l=0.6\mathrm{cm}$ and 1.0 cm, respectively.

Figure 2

Main figure: Critical blister size at onset $B_c$ as a function of $\Gamma /{\delta }^2$. Results from numerical solutions of (2) are shown as points: $\delta ={10}^{-5}$ (○), $\delta ={10}^{-4}$ (□), and $\delta ={10}^{-3}$ (▽) all with $L=500$. The results of the linear theory (solid curve) give rise to the asymptotic results (6). Inset: The functions in the inequality (5) for $\Gamma /{\delta }^2=50$: $f(B)+2\Gamma B/{\delta }^2$ (dashed curve) and $2g(B)$ (solid curve). Blistering is energetically favorable for $B>B_c$. The scaling behaviors of these functions in various limits are also illustrated (see text).

Figure 3

Main figure: Blister size at onset $b_c$ for different sheet thicknesses $h$ measured experimentally (points) and compared to the prediction from numerical computations (solid curve). Inset: The evolution of $B$ with varying compression $\Delta L$. Experimental results are shown for compression (×) and relaxation (○) with the results of the nonlinear theory (solid curve) and the linear result $B\approx 4.844\Delta L^{1/7}$ [1] (dashed curve). The vertical dotted line represents the predicted onset of blistering $\Delta L_c$.