Mechanics of large folds in thin interfacial films

Démery, Vincent; Davidovitch, Benny; Santangelo, Christian

doi:10.1103/physreve.90.042401

Cited by 18 publications

(17 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Seen in this way, one may identify a number of similarities with other interfacial problems. For instance, when a thin film is laterally compressed on a liquid bath, the confining force softens as it undergoes a wrinkle-to-fold transition with large slopes [38,39]. The energy functional [Eq.…”

Section: U N F K L J J H S T H I K C / X 3 R E 5 J Y Y Z X Y D T J I mentioning

confidence: 99%

Geometry underlies the mechanical stiffening and softening of an indented floating film

et al. 2020

Self Cite

View full text Add to dashboard Cite

A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute forces, leading to nonlinear responses rooted in purely geometric effects. Here we identify stiffening and softening as two prominent motifs of such a material-independent, geometrically-nonlinear response of thin sheets, and we show how both effects emanate from nontrivial yet generic features of the stress and displacement fields. Our insights are borne out of studying the indentation of a polymer film on a liquid bath, using experiments, simulations, and theory. We find that stiffening is due to growing anisotropy of the stress field whereas softening is due to changes in shape. We discuss similarities with the mechanics of fiber networks, suggesting that our results are relevant to a wide range of two-and three-dimensional materials.A major challenge in the mechanics of materials and structures is bridging the gap between a system's local material response and its global stiffness. The connection from microscopic to macroscopic scales is often complicated by subtle geometric effects [1]. One conceptually simple example is given by an elastic rod, which may drastically change its shape in response to loading; such elastica problems captured the attention of Galileo, the Bernoullis, and Euler, and variations on it continue to fascinate and push our understanding of slender bodies today [2][3][4]. A twodimensional sheet may also carry tensile loads in one direction while buckling in a perpendicular direction, leading to large anisotropies that control the transmission of forces through the material [5,6]. Understanding such geometrically-nonlinear behaviors is important to a wide range of applications involving thin sheets, from stretchable electronics [7] to large-scale inflatable structures [8]. There is also a diverse array of structures that are essentially composed of many connected rods or sheets, from buckling-or origami-based mechanical metamaterials [9] to soft-robotic systems [10] to disordered networks of elastic fibers including biopolymer gels and the cytoskeleton [11,12]. While much work has been carried out to understand specific systems, much less is known about generic mechanisms underlying their global mechanical response.Here we identify two general types of geometrically-nonlinear behaviors by focusing on the response of a floating thin film to indentation [ Fig. 1a,b], using experiments and simulations spanning four decades in indentation depth and theory that addresses small and large deflections. In the first behavior, the onset of anisotropy in the stress field leads to more effective transmission of forces away from a point of loading, causing the observed force to stiffen (i.e., F/δ increases where F is the force due to the imposed displacement δ) [13]. In the second behavior, the geometry of the deformations causes the transmitted force to saturate at lar...

show abstract

Section: U N F K L J J H S T H I K C / X 3 R E 5 J Y Y Z X Y D T J I mentioning

confidence: 99%

Geometry underlies the mechanical stiffening and softening of an indented floating film

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Beyond a critical compression the wrinkles vanish and localized folds appear in the sheet. Interestingly, the shape of the sheet on the fluid can be found analytically [18][19][20] as long as the sheet does not touch itself [21].…”

Section: Introductionmentioning

confidence: 99%

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

Stoop

Müller

2015

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate.In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.

show abstract

“…We then calculate the membrane response ( p, b) to increased length S. The second assumes the membrane tension is a material parameter (fixed) and the system is 'open' to allow fluid transport through the 'intermembrane space'. It is clear from the comparison of our results that the second scenario most probably governs the mechanics of the inner membrane, whereas the first scenario is potentially relevant to other applications such as wrinkling [26] and folding [27,28] in elastic sheets.…”

Section: Introductionmentioning

confidence: 74%

Elastic membranes in confinement

Bostwick

Miksis

Davis

2016

J. R. Soc. Interface.

View full text Add to dashboard Cite

An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically 'confined' by another object. Here, the two-dimensional shape of an elastic membrane in a 'confining' box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped.

show abstract

Mechanics of large folds in thin interfacial films

Cited by 18 publications

References 27 publications

Geometry underlies the mechanical stiffening and softening of an indented floating film

Geometry underlies the mechanical stiffening and softening of an indented floating film

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

Elastic membranes in confinement

Contact Info

Product

Resources

About