Analysis of the shape of a sheet of paper when two opposite edges are joined

Colom, Antoni Amengual

doi:10.1119/1.2198879

Cited by 5 publications

(2 citation statements)

References 4 publications

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“…19 Indeed, research continues on the contact of an Elastica with a rigid boundary. 20,21 However, the combination of adhesion and large deection elasticity seems only to have been considered for the case of self-contacting 'rackets'. 22,23 In this article, therefore, we consider the form of a blister without the restriction of small slopesthe 'Sticky Elastica'.…”

Section: Introductionmentioning

confidence: 99%

The ‘Sticky Elastica’: delamination blisters beyond small deformations

Wagner

Vella²

2013

Soft Matter

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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.

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Section: Introductionmentioning

confidence: 99%

The ‘Sticky Elastica’: delamination blisters beyond small deformations

Wagner

Vella²

2013

Soft Matter

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“…This would be a bigger problem on thinner sheets of paper with lower values of bending rigidity such as the ones investigated here. Similarly, the work of Colom [20] investigates the bending of rectangular paper strips. Colom presents numerical integration of the pendulum solution to describe the form of a cardioid or various teardrop profile configurations in which the two ends of the paper meet.…”

Section: Introductionmentioning

confidence: 99%

The mechanics of bending a strip of paper

Batista

2020

Eur. J. Phys.

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Here we study the physical problem in which a thin bar, such as a strip of paper, is bent under several types of loads and boundary conditions. Initially, we consider lengthwise compression of the strip due to concentrated forces applied on its ends. We present this problem for the three boundary conditions: doubly-clamped, hinged–clamped, and doubly-hinged ends constrained on a flat surface. We also consider both analytically and experimentally the problems of distributed loading such as the heavy cantilever and the post-buckling heavy column. We find the equations that govern the shapes of the bent strips via a minimization flow of the bending energy. In all cases, we find that photographically-captured profiles agree very well with the theoretical predictions. We also validate the theory with measurements of the deflection of the middle or the tip of the strip as its length is varied.

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