6,382 research outputs found
Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems
We use a conformal mapping method introduced in a companion paper to study
the properties of bi-harmonic fields in the vicinity of rough boundaries. We
focus our analysis on two different situations where such bi-harmonic problems
are encountered: a Stokes flow near a rough wall and the stress distribution on
the rough interface of a material in uni-axial tension. We perform a complete
numerical solution of these two-dimensional problems for any univalued rough
surfaces. We present results for sinusoidal and self-affine surface whose slope
can locally reach 2.5. Beyond the numerical solution we present perturbative
solutions of these problems. We show in particular that at first order in
roughness amplitude, the surface stress of a material in uni-axial tension can
be directly obtained from the Hilbert transform of the local slope. In case of
self-affine surfaces, we show that the stress distribution presents, for large
stresses, a power law tail whose exponent continuously depends on the roughness
amplitude
Permeability of self-affine rough fractures
The permeability of two-dimensional fractures with self-affine fractal
roughness is studied via analytic arguments and numerical simulations. The
limit where the roughness amplitude is small compared with average fracture
aperture is analyzed by a perturbation method, while in the opposite case of
narrow aperture, we use heuristic arguments based on lubrication theory.
Numerical simulations, using the lattice Boltzmann method, are used to examine
the complete range of aperture sizes, and confirm the analytic arguments.Comment: 11 pages, 9 figure
Roughness of fracture surfaces
We study the fracture surface of three dimensional samples through a model
for quasi-static fractures known as Born Model. We find for the roughness
exponent a value of 0.5 expected for ``small length scales'' in microfracturing
experiments. Our simulations confirm that at small length scales the fracture
can be considered as quasi-static. The isotropy of the roughness exponent on
the crack surface is also shown. Finally, considering the crack front, we
compute the roughness exponents for longitudinal and transverse fluctuations of
the crack line (both 0.5). They result in agreement with experimental data, and
supports the possible application of the model of line depinning in the case of
long-range interactions.Comment: 10 pages, 5 figures, Late
Internal states of model isotropic granular packings. III. Elastic properties
In this third and final paper of a series, elastic properties of numerically
simulated isotropic packings of spherical beads assembled by different
procedures and subjected to a varying confining pressure P are investigated. In
addition P, which determines the stiffness of contacts by Hertz's law, elastic
moduli are chiefly sensitive to the coordination number, the possible values of
which are not necessarily correlated with the density. Comparisons of numerical
and experimental results for glass beads in the 10kPa-10MPa range reveal
similar differences between dry samples compacted by vibrations and lubricated
packings. The greater stiffness of the latter, in spite of their lower density,
can hence be attributed to a larger coordination number. Voigt and Reuss bounds
bracket bulk modulus B accurately, but simple estimation schemes fail for shear
modulus G, especially in poorly coordinated configurations under low P.
Tenuous, fragile networks respond differently to changes in load direction, as
compared to load intensity. The shear modulus, in poorly coordinated packings,
tends to vary proportionally to the degree of force indeterminacy per unit
volume. The elastic range extends to small strain intervals, in agreement with
experimental observations. The origins of nonelastic response are discussed. We
conclude that elastic moduli provide access to mechanically important
information about coordination numbers, which escape direct measurement
techniques, and indicate further perspectives.Comment: Published in Physical Review E 25 page
Intermittency of velocity time increments in turbulence
We analyze the statistics of turbulent velocity fluctuations in the time
domain. Three cases are computed numerically and compared: (i) the time traces
of Lagrangian fluid particles in a (3D) turbulent flow (referred to as the
"dynamic" case); (ii) the time evolution of tracers advected by a frozen
turbulent field (the "static" case), and (iii) the evolution in time of the
velocity recorded at a fixed location in an evolving Eulerian velocity field,
as it would be measured by a local probe (referred to as the "virtual probe"
case). We observe that the static case and the virtual probe cases share many
properties with Eulerian velocity statistics. The dynamic (Lagrangian) case is
clearly different; it bears the signature of the global dynamics of the flow.Comment: 5 pages, 3 figures, to appear in PR
Frictionless bead packs have macroscopic friction, but no dilatancy
The statement of the title is shown by numerical simulation of homogeneously
sheared packings of frictionless, nearly rigid beads in the quasistatic limit.
Results coincide for steady flows at constant shear rate γ in the
limit of small γ and static approaches, in which packings are equilibrated
under growing deviator stresses. The internal friction angle ϕ, equal to
5.76 0.22 degrees in simple shear, is independent on the average pressure
P in the rigid limit. It is shown to stem from the ability of stable
frictionless contact networks to form stress-induced anisotropic fabrics. No
enduring strain localization is observed. Dissipation at the macroscopic level
results from repeated network rearrangements, like the effective friction
of a frictionless slider on a bumpy surface. Solid fraction Φ remains
equal to the random close packing value ≃ 0.64 in slowly or statically
sheared systems. Fluctuations of stresses and volume are observed to regress in
the large system limit, and we conclude that the same friction law for simple
shear applies in the large psystem limit if normal stress or density is
externally controlled. Defining the inertia number as I = γ m/(aP),
with m the grain mass and a its diameter, both internal friction
coefficient ∗ = tan ϕ and volume 1/Φ increase as
powers of I in the quasistatic limit of vanishing I, in which all mechanical
properties are determined by contact network geometry. The microstructure of
the sheared material is characterized with a suitable parametrization of the
fabric tensor and measurements of connectivity and coordination numbers
associated with contacts and near neighbors.Comment: 19 pages. Additional technical details may be found in v
An algorithm to calculate the transport exponent in strip geometries
An algorithm for solving the random resistor problem by means of the
transfer-matrix approach is presented. Preconditioning by spanning clusters
extraction both reduces the size of the conductivity matrix and speed up the
calculations.Comment: 17 pages, RevTeX2.1, HLRZ - 97/9
Solid behavior of anisotropic rigid frictionless bead assemblies
We investigate the structure and mechanical behavior of assemblies of
frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by
numerical simulation. Three different loading paths are explored: triaxial
compression, triaxial extension and simple shear. Generalizing recent results
[1], we show that the material, despite rather strong finite sample size
effects, is able to sustain a finite deviator stress in the macroscopic limit,
along all three paths, without dilatancy. The shape of the yield surface is
adequately described by a Lade-Duncan (rather than Mohr-Coulomb) criterion.
While scalar state variables keep the same values as in isotropic systems,
fabric and force anisotropies are each characterized by one parameter and are
in one-to-one correspondence with principal stress ratio along all three
loading paths.The anisotropy of the pair correlation function extends to a
distance between bead surfaces on the order of 10% of the diameter. The tensor
of elastic moduli is shown to possess a nearly singular, uniaxial structure
related to stress anisotropy. Possible stress-strain relations in monotonic
loading paths are also discussed
From Individual to Collective Pinning: Effect of Long-range Elastic Interactions
We study the effect of long-range elastic interactions in the dynamical
behavior of an elastic chain driven quasi-statically in a quenched random
pinning potential and in the strong pinning limit. This is a generic situation
occuring in solid friction, crack propagation, wetting front motion, ... Tuning
the exponent of the algebraic decay of the elastic interaction with the
distance is shown to give rise to three regimes: a Mean-Field (MF) regime, a
Laplacian (L) regime and an intermediate regime where the critical exponents
interpolate continuously between the MF and L limit cases. The effect of the
driving mode on the avalanche statistics is also analyzed.Comment: 28 pages in RevTex, 17 figure
Anisotropic Interface Depinning - Numerical Results
We study numerically a stochastic differential equation describing an
interface driven along the hard direction of an anisotropic random medium. The
interface is subject to a homogeneous driving force, random pinning forces and
the surface tension. In addition, a nonlinear term due to the anisotropy of the
medium is included. The critical exponents characterizing the depinning
transition are determined numerically for a one-dimensional interface. The
results are the same, within errors, as those of the ``Directed Percolation
Depinning'' (DPD) model. We therefore expect that the critical exponents of the
stochastic differential equation are exactly given by the exponents obtained by
a mapping of the DPD model to directed percolation. We find that a moving
interface near the depinning transition is not self-affine and shows a behavior
similar to the DPD model.Comment: 9 pages, 13 figures, REVTe
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