273 research outputs found
Theory of dynamic crack branching in brittle materials
The problem of dynamic symmetric branching of an initial single brittle crack
propagating at a given speed under plane loading conditions is studied within a
continuum mechanics approach. Griffith's energy criterion and the principle of
local symmetry are used to determine the cracks paths. The bifurcation is
predicted at a given critical speed and at a specific branching angle: both
correlated very well with experiments. The curvature of the subsequent branches
is also studied: the sign of , with being the non singular stress at the
initial crack tip, separates branches paths that diverge from or converge to
the initial path, a feature that may be tested in future experiments. The model
rests on a scenario of crack branching with some reasonable assumptions based
on general considerations and in exact dynamic results for anti-plane
branching. It is argued that it is possible to use a static analysis of the
crack bifurcation for plane loading as a good approximation to the dynamical
case. The results are interesting since they explain within a continuum
mechanics approach the main features of the branching instabilities of fast
cracks in brittle materials, i.e. critical speeds, branching angle and the
geometry of subsequent branches paths.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur
Fracture surfaces of heterogeneous materials: a 2D solvable model
Using an elastostatic description of crack growth based on the Griffith
criterion and the principle of local symmetry, we present a stochastic model
describing the propagation of a crack tip in a 2D heterogeneous brittle
material. The model ensures the stability of straight cracks and allows for the
study of the roughening of fracture surfaces. When neglecting the effect of the
non singular stress, the problem becomes exactly solvable and yields analytic
predictions for the power spectrum of the paths. This result suggests an
alternative to the conventional power law analysis often used in the analysis
of experimental data.Comment: 4 pages, 4 figure
Measuring order in the isotropic packing of elastic rods
The packing of elastic bodies has emerged as a paradigm for the study of
macroscopic disordered systems. However, progress is hampered by the lack of
controlled experiments. Here we consider a model experiment for the isotropic
two-dimensional confinement of a rod by a central force. We seek to measure how
ordered is a folded configuration and we identify two key quantities. A
geometrical characterization is given by the number of superposed layers in the
configuration. Using temporal modulations of the confining force, we probe the
mechanical properties of the configuration and we define and measure its
effective compressibility. These two quantities may be used to build a
statistical framework for packed elastic systems.Comment: 4 pages, 5 figure
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
Roughness of tensile crack fronts in heterogenous materials
The dynamics of planar crack fronts in heterogeneous media is studied using a
recently proposed stochastic equation of motion that takes into account
nonlinear effects. The analysis is carried for a moving front in the
quasi-static regime using the Self Consistent Expansion. A continuous dynamical
phase transition between a flat phase and a dynamically rough phase, with a
roughness exponent , is found. The rough phase becomes possible due
to the destabilization of the linear modes by the nonlinear terms. Taking into
account the irreversibility of the crack propagation, we infer that the
roughness exponent found in experiments might become history-dependent, and so
our result gives a lower bound for .Comment: 7 page
Finite-distance singularities in the tearing of thin sheets
We investigate the interaction between two cracks propagating in a thin
sheet. Two different experimental geometries allow us to tear sheets by
imposing an out-of-plane shear loading. We find that two tears converge along
self-similar paths and annihilate each other. These finite-distance
singularities display geometry-dependent similarity exponents, which we
retrieve using scaling arguments based on a balance between the stretching and
the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure
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
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
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