6,302 research outputs found
Friction law and hysteresis in granular materials
The macroscopic friction of particulate materials often weakens as the flow
rate is increased, leading to potentially disastrous intermittent phenomena
including earthquakes and landslides. We theoretically and numerically study
this phenomenon in simple granular materials. We show that velocity-weakening,
corresponding to a non-monotonic behavior in the friction law , is
present even if the dynamic and static microscopic friction coefficients are
identical, but disappears for softer particles. We argue that this instability
is induced by endogenous acoustic noise, which tends to make contacts slide,
leading to faster flow and increased noise. We show that soft spots, or
excitable regions in the materials, correspond to rolling contacts that are
about to slide, whose density is described by a nontrivial exponent .
We build a microscopic theory for the non-monotonicity of , which also
predicts the scaling behavior of acoustic noise, the fraction of sliding
contacts and the sliding velocity, in terms of . Surprisingly,
these quantities have no limit when particles become infinitely hard, as
confirmed numerically. Our analysis rationalizes previously unexplained
observations and makes new experimentally testable predictions.Comment: 6 pages + 3 pages S
Non-equilibrium thermodynamical framework for rate- and state-dependent friction
Rate- and state-dependent friction law for velocity-step and healing are
analysed from a thermodynamic point of view. Assuming a logarithmic deviation
from steady-state a unification of the classical Dieterich and Ruina models of
rock friction is proposed.Comment: 12 pages, 5 figure
Unsteady 3D-Navier-Stokes System with Tresca's Friction Law
Motivated by extrusion problems, we consider a non-stationary incompress-ible
3D fluid flow with a non-constant (temperature dependent) viscosity, subjected
to mixed boundary conditions with a given time dependent velocity on a part of
the boundary and Tresca's friction law on the other part. We construct a
sequence of approximate solutions by using a regularization of the free
boundary condition due to friction combined with a particular penalty method,
reminiscent of the " incompressibility limit " of compressible fluids, allowing
to get better insights into the links between the fluid velocity and pressure
fields. Then we pass to the limit with compactness arguments to obtain a
solution to our original problem
Self-Similarity of Friction Laws
The change of the friction law from a mesoscopic level to a macroscopic level
is studied in the spring-block models introduced by Burridge-Knopoff. We find
that the Coulomb law is always scale invariant. Other proposed scaling laws are
only invariant under certain conditions.}Comment: Plain TEX. Figures not include
Nonlinear shear wave interaction at a frictional interface: Energy dissipation and generation of harmonics
Analytical and numerical modelling of the nonlinear interaction of shear wave
with a frictional interface is presented. The system studied is composed of two
homogeneous and isotropic elastic solids, brought into frictional contact by
remote normal compression. A shear wave, either time harmonic or a narrow band
pulse, is incident normal to the interface and propagates through the contact.
Two friction laws are considered and their influence on interface behavior is
investigated : Coulomb's law with a constant friction coefficient and a
slip-weakening friction law which involves static and dynamic friction
coefficients. The relationship between the nonlinear harmonics and the
dissipated energy, and their dependence on the contact dynamics (friction law,
sliding and tangential stress) and on the normal contact stress are examined in
detail. The analytical and numerical results indicate universal type laws for
the amplitude of the higher harmonics and for the dissipated energy, properly
non-dimensionalized in terms of the pre-stress, the friction coefficient and
the incident amplitude. The results suggest that measurements of higher
harmonics can be used to quantify friction and dissipation effects of a sliding
interface.Comment: 17 pages, 10 figure
Thermodynamic aspects of rock friction
Rate- and state-dependent friction law for velocity-step tests is analyzed
from a thermodynamic point of view. A simple macroscopic non-equilibrium
thermodynamic model with a single internal variable reproduces instantaneous
jump and relaxation. Velocity weakening appears as a consequence of a
plasticity related nonlinear coefficient. Permanent part of displacement
corresponds to plastic strain, and relaxation effects are analogous to creep in
thermodynamic rheology.Comment: 13 pages 3 figures. Revision: thermodynamic compatibility of velocity
weakenin
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