Julien Chopin

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 Föppl–von Kármán 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.

Tension-dependent transverse buckles and wrinkles in twisted elastic sheets

We investigate with experiments the twist-induced transverse buckling instabilities of an elastic sheet of length L, width W and thickness t, that is clamped at two opposite ends while held under a tension T. Above a critical tension Tλ and critical twist angle ηtr, we find that the sheet buckles with a mode number n≥1 transverse to the axis of twist. Three distinct buckling regimes characterized as clamp-dominated, bendable and stiff are identified, by introducing a bendability length LB and a clamp length LC(<LB). In the stiff regime (L>LB), we find that mode n=1 develops above ηtr≡ηS∼(t/W)T−1/2, independent of L. In the bendable regime LC<L<LB, n=1 as well as n>1 occur above ηtr≡ηB∼t/LT−1/4. Here, we find the wavelength λB∼LtT−1/4, when n>1. These scalings agree with those derived from a covariant form of the Föppl-von Kármán equations, however, we find that the n=1 mode also occurs over a surprisingly large range of L in the bendable regime. Finally, in the clamp-dominated regime (L<LC), we find that ηtr is higher compared to ηB due to additional stiffening induced by the clamped boundary conditions.

Dynamic Wrinkling and Strengthening of an Elastic Filament in a Viscous Fluid

We investigate the wrinkling dynamics of an elastic filament immersed in a viscous fluid submitted to compression at a finite rate with experiments and by combining geometric nonlinearities, elasticity, and slender body theory. The drag induces a dynamic lateral reinforcement of the filament leading to growth of wrinkles that coarsen over time. We discover a new dynamical regime characterized by a time scale with a nontrivial dependence on the loading rate, where the growth of the instability is superexponential and the wave number is an increasing function of the loading rate. We find that this time scale can be interpreted as the characteristic time over which the filament transitions from the extensible to the inextensible regime. In contrast with our analysis with moving boundary conditions, Biots analysis in the limit of infinitely fast loading leads to rate independent exponential growth and wavelength.