Dynamic effective mass of granular media

Bottom pressure scaling of vibro-fluidized granular matter

Vibrated granular beds show various interesting phenomena such as convection, segregation, and so on. However, its fundamental physical properties (e.g., internal pressure structure) have not yet been understood well. Thus, in this study, the bottom wall pressure in a vertically vibrated granular column is experimentally measured and used to reveal the nature of granular fluidization. The scaling method allows us to elucidate the fluidization (softening) degree of a vibrated granular column. The peak value of the bottom pressure pm is scaled as [formula in text], where pJ, d, g, ω, H, and Γ are the Janssen pressure, grain diameter, gravitational acceleration, angular frequency, height of the column, and dimensionless vibrational acceleration, respectively. This scaling implies that the pressure of vibrated granular matter is quite different from the classical pressure forms: static and dynamic pressures. This scaling represents the importance of geometric factors for discussing the behavior of vibro-fluidized granular matter. The scaling is also useful to evaluate the dissipation degree in vibro-fluidized granular matter.

Density of states in granular media in the presence of damping

We consider the density of states of granular media in which each grain-grain contact is damped with a damping force proportional to the relative velocity of the two grains, in addition to the usual spring constant. Under the assumption that the so-called criterion of proportional damping is only weakly violated we are able to deduce the density of states for undamped frequencies from the measured complex-valued frequencies of damped oscillations. We deduce a quantitative estimate of the deviation from the proportional criterion. We consider, specifically, numerical simulations of cases in which the grains are frictionless spheres that interact via Hertz central forces and all the nonzero contacts are damped with the same damping constant. We show how these ideas can be applied to data on real granular systems.

Celebrating Soft Matter's 10th Anniversary: toward jamming by design

In materials science, high performance is typically associated with regularity and order, while disorder and the presence of defects are assumed to lead to sub-optimal outcomes. This holds for traditional solids such as crystals as well as for many types of nanoscale devices. However, there are circumstances where disorder can be harnessed to achieve performance not possible with approaches based on regularity. Recent research has shown opportunities specifically for soft matter. There, the phenomenon of jamming leads to unique emergent behavior that enables disordered, amorphous systems to switch reversibly between solid-like rigidity and fluid-like plasticity. This makes it possible to envision materials that can change stiffness or even shape adaptively. We review some of the progress in this direction, discussing examples where jamming has been explored from micro to macro scales in colloidal systems, suspensions, granular-materials-enabled soft robotics, and architecture. We focus in particular on how the jammed aggregate state can be tailored by controlling particle level properties and discuss very recent ideas that provide an important first step toward actual design of specifically targeted jamming behavior.

Stress-dependent normal-mode frequencies from the effective mass of granular matter

A zero-temperature critical point has been invoked to control the anomalous behavior of granular matter as it approaches jamming or mechanical arrest. Criticality manifests itself in an anomalous spectrum of low-frequency normal modes and scaling behavior near the jamming transition. The critical point may explain the peculiar mechanical properties of dissimilar systems such as glasses and granular materials. Here we study the critical scenario via an experimental measurement of the normal modes frequencies of granular matter under stress from a pole decomposition analysis of the effective mass. We extract a complex-valued characteristic frequency which displays scaling |ω (σ)| ∼ σΩ' with vanishing stress σ for a variety of granular systems. The critical exponent is smaller than that predicted by mean-field theory opening new challenges to explain the exponent for frictional and dissipative granular matter. Our results shed light on the anomalous behavior of stress-dependent acoustics and attenuation in granular materials near the jamming transition.

Hypocoordinated solids in particulate media

We propose a "phase diagram" for particulate systems with purely repulsive contact forces, such as granular media and colloids. We characterize two classes of behavior as a function of the input kinetic energy per degree of freedom T_{0} and packing fraction deviation from jamming onset Δϕ=ϕ-ϕ_{J} using simulations of frictionless disks. Isocoordinated solids (ICS) exist above jamming; they possess an average contact number equal to the isostatic value z_{iso}. ICS display "strict" harmonic response, where the density of vibrational modes from the Fourier transform of the velocity autocorrelation function is a set of sharp peaks at eigenfrequencies ω_{k}{d} of the dynamical matrix. In contrast, hypocoordinated solids (HCS) occur above and below jamming and possess fluctuating networks of interparticle contacts but do not undergo cage-breaking particle rearrangements. The density of vibrational frequencies for the HCS is not a collection of sharp peaks at ω_{k}{d}, but it does possess a common form over a range of Δϕ and T_{0}.

Edwards thermodynamics of the jamming transition for frictionless packings: ergodicity test and role of angoricity and compactivity

This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and "thermalization" at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A → 0+ and X → 0-. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a "jamming temperature" T(J) composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O'Hern [Phys. Rev. E 74, 061304 (2006)], showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other out-of-equilibrium systems like Lennard-Jones glasses and their existence does not preclude the use of statistical mechanics for jammed systems.

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.

Effect of granular media on the vibrational response of a resonant structure: theory and experiment

The acoustic response of a structure that contains a cavity filled with a loose granular material is analyzed. The inputs to the theory are the effective masses of each subsystem: that of the empty-cavity resonating structure and that of the granular medium within the cavity. This theory accurately predicts the frequencies, widths, and relative amplitudes of the various flexural mode resonances observed with rectangular bars, each having a cavity filled with loose tungsten granules. Inasmuch as the dominant mechanism for damping is due to adsorbed water at the grain-grain contacts, the significant effects of humidity on both the effective mass of the granular medium as well as on the response of the grain-loaded bars are monitored. Here, depending upon the humidity and the preparation protocol, it is possible to observe one, two, or three distinct resonances in a wide frequency range (1-5 kHz) over which the empty bar has but one resonance. These effects are understood in terms of the theoretical framework, which may simplify in terms of perturbation theories.

Dynamic effective mass of granular media and the attenuation of structure-borne sound

We report a theoretical and experimental investigation into the fundamental physics of why loose granular media are effective deadeners of structure-borne sound. Here, we demonstrate that a measurement of the effective mass, M(omega), of the granular medium is a sensitive and direct way to answer the question: what is the specific mechanism whereby acoustic energy is transformed into heat? Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The pore space in the granular medium is air of varying humidity. The dominant features of M(omega) are a sharp resonance and a broad background, which we analyze within the context of simple models. We find that: (a) on a fundamental level, dampening of acoustic modes is dominated by adsorbed films of water at grain-grain contacts, not by global viscous dampening or by attenuation within the grains. (b) These systems may be understood, qualitatively, in terms of a height-dependent and diameter-dependent effective sound speed [approximately 100-300 (m.s-1)] and an effective viscosity [approximately 5x10(4) Poise]. (c) There is an acoustic Janssen effect in the sense that, at any frequency, and depending on the method of sample preparation, approximately one-half of the effective mass is borne by the side walls of the cavity and one-half by the bottom. (d) There is a monotonically increasing effect of humidity on the dampening of the fundamental resonance within the granular medium which translates to a nonmonotonic, but predictable, variation in dampening within the grain-loaded bar.