The ‘Sticky Elastica’: delamination blisters beyond small deformations

Abstract

We consider the form of an elastic loop adhered to a rigid substrate: the 'sticky Elastica'. In contrast to previous studies of the shape of delamination 'blisters', the theory developed accounts for deflections with large slope (i.e. geometrically nonlinear). Starting from the classical Euler Elastica we provide numerical results for the dimensions of such blisters for a variety of end-end confinements and develop asymptotic expressions that reproduce these results well up to the point of self-contact. Interestingly, we find that the width of such blisters does not grow monotonically with increased confinement. Our theoretical predictions are confirmed by simple desktop experiments and suggest a new method for the measurement of the elastocapillary length for deformations that cannot be considered small.

Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

“…From the boundary condition (9c) we find H = − 4f s 2 c for −1 <s < 1. In particular in the middle of the fold (s = 0) we thus obtain for each order π ≈ 2.92 (32) or f (0) = 20/ √ 3 ≈ 11.55. The angle ψ (1) at linear order follows as…”

“…Similar to a ruck in a rug [29][30][31][32] we will consider the case in which the sheet can slide on the cylinder. The only coupling between the sheet and the substrate is via the hard cylinder constraint.…”

The delamination of a growing elastic sheet with adhesion

“…Blisters in a thin structure can form essentially for two reasons: (i) the two far edges of the strip are brought closer [5,6] or (ii) there exists an incompatibility between the geometries of the sheet and substrate. Such a mismatch can be induced, for instance, by thermal dilatation or by growth.…”

Snap buckling of a confined thin elastic sheet

“…The collapse of an elastic sheet adhered to a curved substrate is certainly one of them. This discontinuous buckling instability appears in various problems in biology (shapes and morphogenesis of the mitochondrion (Sakashita et al, 2014)), physics (packing of thin films (Boué et al, 2006), delamination of thin elastic films (Vella et al, 2009;Wagner and Vella, 2013), design of stretchable electronic devices (Sun et al, 2006), elastocapillary snapping (Fargette et al, 2014)) and engineering (collapse of buried steel pipelines (Omara et al, 1997;Vasilikis and Karamanos, 2009)).…”