48 research outputs found
Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume
Naturally-occurring granular materials often consist of angular particles
whose shape and frictional characteristics may have important implications on
macroscopic flow rheology. In this paper, we provide a theoretical account for
the peculiar phenomenon of auto-acoustic compaction -- non-monotonic variation
of shear band volume with shear rate in angular particles -- recently observed
in experiments. Our approach is based on the notion that the volume of a
granular material is determined by an effective-disorder temperature known as
the compactivity. Noise sources in a driven granular material couple its
various degrees of freedom and the environment, causing the flow of entropy
between them. The grain-scale dynamics is described by the
shear-transformation-zone (STZ) theory of granular flow, which accounts for
irreversible plastic deformation in terms of localized flow defects whose
density is governed by the state of configurational disorder. To model the
effects of grain shape and frictional characteristics, we propose an Ising-like
internal variable to account for nearest-neighbor grain interlocking and
geometric frustration, and interpret the effect of friction as an acoustic
noise strength. We show quantitative agreement between experimental
measurements and theoretical predictions, and propose additional experiments
that provide stringent tests on the new theoretical elements.Comment: 12 pages, 3 figure
Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations
We propose a theory of shear flow in dense granular materials. A key
ingredient of the theory is an effective temperature that determines how the
material responds to external driving forces such as shear stresses and
vibrations. We show that, within our model, friction between grains produces
stick-slip behavior at intermediate shear rates, even if the material is
rate-strengthening at larger rates. In addition, externally generated acoustic
vibrations alter the stick-slip amplitude, or suppress stick-slip altogether,
depending on the pressure and shear rate. We construct a phase diagram that
indicates the parameter regimes for which stick-slip occurs in the presence and
absence of acoustic vibrations of a fixed amplitude and frequency. These
results connect the microscopic physics to macroscopic dynamics, and thus
produce useful information about a variety of granular phenomena including
rupture and slip along earthquake faults, the remote triggering of
instabilities, and the control of friction in material processing.Comment: 12 pages, 8 figure
A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults
Despite its critical role in the study of earthquake processes, numerical
simulation of the entire stages of fault rupture remains a formidable task. The
main challenges in simulating a fault rupture process include complex evolution
of fault geometry, frictional contact, and off-fault damage over a wide range
of spatial and temporal scales. Here, we develop a phase-field model for
quasi-dynamic fault nucleation, growth, and propagation, which features two
standout advantages: (i) it does not require any sophisticated algorithms to
represent fault geometry and its evolution; and (ii) it allows for modeling
fault nucleation, propagation, and off-fault damage processes with a single
formulation. Built on a recently developed phase-field framework for shear
fractures with frictional contact, the proposed formulation incorporates rate-
and state-dependent friction, radiation damping, and their impacts on fault
mechanics and off-fault damage. We show that the numerical results of the
phase-field model are consistent with those obtained from well-verified
approaches that model the fault as a surface of discontinuity, without
suffering from the mesh convergence issue in the existing continuous approaches
to fault rupture (e.g. the stress glut method). Further, through numerical
examples of fault propagation in various settings, we demonstrate that the
phase-field approach may open new opportunities for investigating complex
earthquake processes that have remained overly challenging for the existing
numerical methods
A new paradigm for simulating pulse-like ruptures: the pulse energy equation
We investigate the chaotic behaviour of slip pulses that propagate in a spring block slider
model with velocity weakening friction by numerically solving a computationally intensive
set of n coupled non-linear equations, where n is the number of blocks. We observe that the
system evolves into a spatially heterogeneous pre-stress after the occurrence of a sufficient
number of events. We observe that, although the spatiotemporal evolution of the amplitude of
a slip pulse in a single event is surprisingly complex, the geometric description of the pulses
is simple and self-similar with respect to the size of the pulse. This observation allows us to
write an energy balance equation that describes the evolution of the pulse as it propagates
through the known pre-stress. The equation predicts the evolution of individual ruptures and
reduces the computational time dramatically. The long-time solution of the equation reveals
its multiscale nature and its potential to match many of the long-time statistics of the original
system, but with a much shorter computational time
Experimental Evidence of Amplitude-Dependent Surface Wave Dispersion via Nonlinear Contact Resonances
In this letter, we provide an experimental demonstration of
amplitude-dependent dispersion tuning of surface acoustic waves interacting
with nonlinear resonators. Leveraging the similarity between the dispersion
properties of plate edge waves and surface waves propagating in a semi-infinite
medium, we use a setup consisting of a plate with a periodic arrangement of
bead-magnet resonators along one of its edges. Nonlinear contact between the
ferromagnetic beads and magnets is exploited to realize nonlinear local
resonance effects. First, we experimentally demonstrate the nonlinear softening
nature and amplitude-dependent dynamics of a single bead-magnet resonator on
both rigid and compliant substrates. Next, the dispersion properties of the
system in the linear regime are investigated. Finally, we demonstrate how the
interplay of nonlinear local resonances with plate edge waves gives rise to
amplitude-dependent dispersion properties. The findings will inform the design
of more versatile surface acoustic wave devices that can passively adapt to
loading conditions.Comment: 6 pages, 5 figures, 2 table