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Register a new userLocalization and instability in sheared granular materials: Role of friction and vibration
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Shear banding and stick-slip instabilities have been long observed in sheared granular materials. Yet, their microscopic underpinnings, interdependencies and variability under different loading conditions have not been fully explored. Here, we use a non-equilibrium thermodynamics model, the Shear Transformation Zone theory, to investigate the dynamics of strain localization and its connection to stability of sliding in sheared, dry, granular materials. We consider frictional and frictionless grains as well as presence and absence of acoustic vibrations. Our results suggest that at low and intermediate strain rates, persistent shear bands develop only in the absence of vibrations. Vibrations tend to fluidize the granular network and de-localize slip at these rates. Stick-slip is only observed for frictional grains and it is confined to the shear band. At high strain rates, stick-slip disappears and the different systems exhibit similar stress-slip response. Changing the vibration intensity, duration or time of application alters the system response and may cause long-lasting rheological changes. We analyse these observations in terms of possible transitions between rate strengthening and rate weakening response facilitated by a competition between shear induced dilation and vibration induced compaction. We discuss the implications of our results on dynamic triggering, quiescence and strength evolution in gouge filled fault zones.
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We report results of 3D Discrete Element Method (DEM) simulations aiming at investigating the role of the boundary vibration in inducing frictional weakening in sheared granular layers. We study the role of different vibration amplitudes applied at various shear stress levels, for a granular layer in the stick-slip regime and in the steady-sliding regime. Results are reported in terms of friction drops and kinetic energy release associated with frictional weakening events. We find that larger vibration amplitude induces larger frictional weakening events. The results show evidence of a threshold below which no induced frictional weakening takes place. Friction drop size is found to be dependent on the shear stress at the time of vibration. A significant increase in the ratio between the number of slipping contacts to the number of sticking contacts in the granular layer is observed for large vibration amplitudes. These vibration-induced contact rearrangements enhance particle mobilization and induces a friction drop and kinetic energy release. This observation provides some insight into the grain-scale mechanisms of frictional weakening by boundary vibration in a dense sheared granular layer. In addition to characterizing the basic physics of vibration induced shear weakening, we are attempting to understand how a fault fails in the earth under seismic wave forcing. This is the well know phenomenon of dynamic earthquake triggering. We believe that the granular physics are key to this understanding.
The coupled mechanics of fluid-filled granular media controls the behavior of many natural systems such as saturated soils, fault gouge, and landslides. The grain motion and the fluid pressure influence each other: It is well established that when the fluid pressure rises, the shear resistance of fluid-filled granular systems decreases, and as a result catastrophic events such as soil liquefaction, earthquakes, and accelerating landslides may be triggered. Alternatively, when the pore pressure drops, the shear resistance of these systems increases. Despite the great importance of the coupled mechanics of grains-fluid systems, the basic physics that controls this coupling is far from understood. We developed a new multi-scaled model based on the discrete element method, coupled with a continuum model of fluid pressure, to explore this dynamical system. The model was shown recently to capture essential feedbacks between porosity changes arising from rearrangement of grains, and local pressure variations due to changing pore configurations. We report here new results from numerical experiments of a continuously shearing layer of circular two-dimensional grains, trapped between two parallel rough boundaries. The experiments use a fixed confining stress on the boundary walls, and a constant velocity applied to one of the boundaries, as if this system was the interior of a sliding geological fault filled with fault gouge. In addition, we control the layer permeability and the drainage boundary conditions. This paper presents modeling results showing that the localization of shear (into a narrow shear band within the shearing layer) is strongly affected by the presence of fluids. While in dry granular layers there is no preferred position for the onset of localization, drained systems tend to localize shear on their boundary. We propose a scaling argument to describe the pressure deviations in a shear band, and use that to predict the allowable positions of shear localizations as a function of the fault and gouge properties.
We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilised, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.
Motion stages are widely used for precision positioning in manufacturing and metrology applications. However, they suffer from nonlinear premotion (i.e. static) friction, which adversely affects their speed and motion precision. In this article, a friction isolator is used as a simple and robust solution to mitigate the undesirable effects of premotion friction in precision motion stages. For the first time, a theoretical study is carried out to understand the dynamic phenomena associated with using a friction isolator on a motion stage. Theoretical analysis and numerical simulation are conducted to examine the dynamical effects of friction isolator on a proportional-integral-derivative-controlled motion stage under LuGre friction dynamics. The influence of friction isolator on the response and stability of the system is examined through theoretical and numerical analyses. Parametric analysis is also carried out to study the effects of friction isolator and friction parameters on the eigenvalue and stability characteristics. The numerical results validate the theoretical findings and demonstrate several other interesting nonlinear phenomena associated with the introduction of friction isolator. This motivates deeper nonlinear dynamical analyses of friction isolator for precision motion control.
We use the Discrete Element Method (DEM) to understand the underlying attenuation mechanism in granular media, with special applicability to the measurements of the so-called effective mass developed earlier. We consider that the particles interact via Hertz-Mindlin elastic contact forces and that the damping is describable as a force proportional to the velocity difference of contacting grains. We determine the behavior of the complex-valued normal mode frequencies using 1) DEM, 2) direct diagonalization of the relevant matrix, and 3) a numerical search for the zeros of the relevant determinant. All three methods are in strong agreement with each other. The real and the imaginary parts of each normal mode frequency characterize the elastic and the dissipative properties, respectively, of the granular medium. We demonstrate that, as the interparticle damping, $xi$, increases, the normal modes exhibit nearly circular trajectories in the complex frequency plane and that for a given value of $xi$ they all lie on or near a circle of radius $R$ centered on the point $-iR$ in the complex plane, where $Rpropto 1/xi$. We show that each normal mode becomes critically damped at a value of the damping parameter $xi approx 1/omega_n^0$, where $omega_n^0$ is the (real-valued) frequency when there is no damping. The strong indication is that these conclusions carry over to the properties of real granular media whose dissipation is dominated by the relative motion of contacting grains. For example, compressional or shear waves in unconsolidated dry sediments can be expected to become overdamped beyond a critical frequency, depending upon the strength of the intergranular damping constant.
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