510 research outputs found
Cloaking by coating: How effectively does a thin, stiff coating hide a soft substrate?
From human tissue to fruits, many soft materials are coated by a thin layer
of a stiffer material. While the primary role of such a coating is often to
protect the softer material, the thin, stiff coating also has an important
effect on the mechanical behaviour of the composite material, making it appear
significantly stiffer than the underlying material. We study this cloaking
effect of a coating for the particular case of indentation tests, which measure
the `firmness' of the composite solid: we use a combination of theory and
experiment to characterize the firmness quantitatively. We find that the
indenter size plays a key role in determining the effectiveness of cloaking:
small indenters feel a mixture of the material properties of the coating and of
the substrate, while large indenters sense largely the unadulterated substrate
Far From Threshold Buckling Analysis of Thin Films
Thin films buckle easily and form wrinkled states in regions of well defined
size. The extent of a wrinkled region is typically assumed to reflect the zone
of in-plane compressive stresses prior to buckling, but recent experiments on
ultrathin sheets have shown that wrinkling patterns are significantly longer
and follow different scaling laws than those predicted by standard buckling
theory. Here we focus on a simple setup to show the striking differences
between near-threshold buckling and the analysis of wrinkle patterns in very
thin films, which are typically far from threshold.Comment: 4 page
A comparative study of crumpling and folding of thin sheets
Crumpling and folding of paper are at rst sight very di erent ways of con
ning thin sheets in a small volume: the former one is random and stochastic
whereas the latest one is regular and deterministic. Nevertheless, certain
similarities exist. Crumpling is surprisingly ine cient: a typical crumpled
paper ball in a waste-bin consists of as much as 80% air. Similarly, if one
folds a sheet of paper repeatedly in two, the necessary force becomes so large
that it is impossible to fold it more than 6 or 7 times. Here we show that the
sti ness that builds up in the two processes is of the same nature, and
therefore simple folding models allow to capture also the main features of
crumpling. An original geometrical approach shows that crumpling is
hierarchical, just as the repeated folding. For both processes the number of
layers increases with the degree of compaction. We nd that for both processes
the crumpling force increases as a power law with the number of folded layers,
and that the dimensionality of the compaction process (crumpling or folding)
controls the exponent of the scaling law between the force and the compaction
ratio.Comment: 5 page
A prototypical model for tensional wrinkling in thin sheets
The buckling and wrinkling of thin films has recently seen a surge of interest among physicists, biologists, mathematicians and engineers. This has been triggered by the growing interest in developing technologies at ever decreasing scales and the resulting necessity to control the mechanics of tiny structures, as well as by the realization that morphogenetic processes, such as the tissue-shaping instabilities occurring in animal epithelia or plant leaves, often emerge from mechanical instabilities of cell sheets. While the most basic buckling instability of uniaxially compressed plates was understood by Euler more than 200 years ago, recent experiments on nanometrically thin (ultrathin) films have shown significant deviations from predictions of standard buckling theory. Motivated by this puzzle, we introduce here a theoretical model that allows for a systematic analysis of wrinkling in sheets far from their instability threshold. We focus on the simplest extension of Euler buckling that exhibits wrinkles of finite length - a sheet under axisymmetric tensile loads. This geometry, whose first study is attributed to LamÂŽe, allows us to construct\ud
a phase diagram that demonstrates the dramatic variation of wrinkling patterns from near-threshold to far-from-threshold conditions. Theoretical arguments and comparison to experiments show that for thin sheets the far-from-threshold regime is expected to emerge under extremely small compressive loads, emphasizing the relevance of our analysis for nanomechanics applications
Dynamic stability of crack fronts: Out-of-plane corrugations
The dynamics and stability of brittle cracks are not yet fully understood.
Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys.
Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar
crack fronts in the framework of linear elastic fracture mechanics. We discuss
a minimal scenario in which linearly unstable crack front corrugations might
emerge above a critical front propagation speed. We calculate this speed as a
function of Poisson's ratio and show that corrugations propagate along the
crack front at nearly the Rayleigh wave-speed. Finally, we hypothesize about a
possible relation between such corrugations and the long-standing problem of
crack branching.Comment: 5 pages, 2 figures + supplementary informatio
Capillary deformations of bendable films
We address the partial wetting of liquid drops on ultrathin solid sheets resting on a deformable foundation. Considering the membrane limit of sheets that can relax compression through wrinkling at negligible energetic cost, we revisit the classical theory for the contact of liquid drops on solids. Our calculations and experiments show that the liquid-solid-vapor contact angle is modified from the Young angle, even though the elastic bulk modulus (E) of the sheet is so large that the ratio between the surface tension Îł and E is of molecular size. This finding establishes a new type of âsoft capillarityâ that stems from the bendability of thin elastic bodies rather than from material softness. We also show that the size of the wrinkle pattern that emerges in the sheet is fully predictable, thus resolving a puzzle noticed in several previous attempts to model âdrop-on-a-floating-sheetâ experiments, and enabling a reliable usage of this setup for the metrology of ultrathin films
Solution of the Percus-Yevick equation for hard discs
We solve the Percus-Yevick equation in two dimensions by reducing it to a set
of simple integral equations. We numerically obtain both the pair correlation
function and the equation of state for a hard disc fluid and find good
agreement with available Monte-Carlo calculations. The present method of
resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure
Oscillatory fracture path in thin elastic sheet
We report a novel mode of oscillatory crack propagation when a cutting tip is
driven through a thin brittle polymer film. The phenomenon is so robust that it
can easily be reproduced at hand (using CD packaging material for example).
Careful experiments show that the amplitude and wavelength of the oscillatory
crack path scale lineraly with the width of the cutting tip over a wide range
of lenghtscales but are independant of the width of thje sheet and the cutting
speed. A simple geometric model is presented, which provides a simple but
thorough interpretation of the oscillations.Comment: 6 pages, submitted to Comptes Rendus Academie des Sciences. Movies
available at http://www.lmm.jussieu.fr/platefractur
First Order Phase Transition of a Long Polymer Chain
We consider a model consisting of a self-avoiding polygon occupying a
variable density of the sites of a square lattice. A fixed energy is associated
with each -bend of the polygon. We use a grand canonical ensemble,
introducing parameters and to control average density and average
(total) energy of the polygon, and show by Monte Carlo simulation that the
model has a first order, nematic phase transition across a curve in the
- plane.Comment: 11 pages, 7 figure
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