Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session U29: Focus Session: Jamming: Marginal Solids II |
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Sponsoring Units: GSNP Chair: Joshua Dijksman, Duke University Room: 337 |
Thursday, March 21, 2013 11:15AM - 11:51AM |
U29.00001: Shear jamming in granular materials Invited Speaker: Jie Zhang For frictionless particles with purely repulsive interactions, there is a critical packing fraction $\phi_J$ below which no jammed states exist. Frictional granular particles in the regime of $\phi < \phi_J$ act differently under shear: early experiments by Zhang \& Behringer at Duke University show jammed states can be created by the application of shear stress. Compared to the states above $\phi_J$, the shear-jammed states (SJS) are mechanically more fragile, but they can resist shear. Formation of these states requires the anisotropic contact network as a backbone and these new states must be incorporated into a more general jamming picture (Bi et al Nature 2011). If time permits, I will present some new results from recent experiments at SJTU aimed towards understanding the more detailed nature of SJS and the transition from unjammed states to SJS. [Preview Abstract] |
Thursday, March 21, 2013 11:51AM - 12:03PM |
U29.00002: Compression and Shear Driven Jamming of Frictionless U-Shaped Particles in Two Dimensions Theodore Marschall, Andrew Loheac, Scott Franklin, Stephen Teitel We simulate a system of soft, frictionless, U-shaped particles (staples), under both isotropic compression and uniform shear flow in two dimensions. The shape of the particles allows them to interlock, causing a geometry induced particle cohesion. We investigate the jamming transition of this system as the packing fraction is increased, in an effort to learn whether such geometric cohesion in novel shaped frictionless particles can produce effects similar to what is found for frictional smooth disks. [Preview Abstract] |
Thursday, March 21, 2013 12:03PM - 12:15PM |
U29.00003: Shear Reversibility in Model Granular Systems Carl Schreck, Rob Hoy, Mark Shattuck, Corey O'Hern Athermal particulate systems such as foams and granular media are out-of-thermal equilibrium and therefore must be externally driven using shear or vibration to explore different configurations. Of particular interest is being able to predict and control the structural and mechanical properties of athermal systems as a function of the driving mechanism. In this work, we show numerically how particle collisions in cyclically sheared hard sphere systems can lead to microreversibility. We map out the steady-state ``phase diagram'' as a function of packing fraction ($\phi$) and strain amplitude ($\gamma_{max}$), and identify ``point-reversible'' states at low $\phi$ and $\gamma_{max}$ in which particles do not collide over the course of a shear cycle, and ``loop-reversible'' states at intermediate $\phi$ and $\gamma_{max}$ in which particles undergo numerous collisions but return to their initial positions at the end of each shear cycle. Loop-reversiblity is a novel form of self organization that gives rise to non-fluctuating dynamical states over a broad range of packing fractions from contact percolation to jamming, i.e. $\phi_P=0.55$ to $\phi_J=0.84$ in two dimensions. [Preview Abstract] |
Thursday, March 21, 2013 12:15PM - 12:27PM |
U29.00004: Stress dynamics of a 2D dense granular system near shear jamming Jie Ren, Joshua Dijksman, Robert Behringer We study the dynamics of pressure and shear stress in a frictional 2D dense granular system using a novel apparatus that can provide fixed-volume shear without generating inhomogeneities. Under increasing shear strain, the system's pressure shows a strong increase with strain, characterized by a ``Reynolds coefficient,'' $R = d^2 P / d \gamma ^2$. R depends only on packing fraction $\phi$, and shows a strong increase as $\phi$ approaches $\phi_J$ from below. In the meantime, the system's shear stress shows a non-monotonic behavior with increasing strain. It first increases with strain as the system is in ``fragile'' states and builds up long force chains along the compression direction. After a certain amount of strain, force chains along the dilation direction starts to build up, and the system transfers into a ``shear-jammed'' state and the shear stress starts to decrease with strain. Under oscillatory shear, both pressure and shear stress show limit-cycle behavior and reach steady states after many cycles. However, the limit cycles of pressure and shear stress are very different: the pressure exhibits a hysteresis-free parabolic curve, while the shear stress exhibits a strongly hysteretic loop. [Preview Abstract] |
Thursday, March 21, 2013 12:27PM - 12:39PM |
U29.00005: Shear jamming in a two dimensional granular system without basal friction Hu Zheng, Joshua Dijksman, Robert Behringer Two dimensional granular systems are an important tool to explore the dynamics of granular materials. However, traditional experimental methods could not avoid the effects of friction between particles and the base on which they rest. Here, we develop a novel apparatus which allows us to tune the basal friction of the particles. We do so by submersing the particles in a density matched liquid, thus removing the normal force, hence the friction, between the particles and base. We use this technique to investigate the effect of shear jamming found by Bi et. al. (2011) by probing the overall shear stress, particle motion and the photoelastic response of the particles under simple shear. [Preview Abstract] |
Thursday, March 21, 2013 12:39PM - 12:51PM |
U29.00006: Bagnold and linear scalings in shearing simulations of massive particles Daniel V{\aa}gberg, Peter Olsson, S. Teitel We consider the rheology of massive bidisperse soft-core discs in two dimensions driven by a constant shear rate $\dot\gamma$ at zero temperature. We study how the behavior depends on the details of the dynamics, by investigating three different models for the energy dissipation. In these models the dissipation from two colliding particles are proportional to (1) the total velocity difference, (2) the normal component of the velocity difference, (3) the tangential component of the velocity difference, respectively. It turns out that these seemingly minor differences have major implications for the scaling of the pressure $p$ with respect to $\dot\gamma$. The system can exhibit linear scaling, $p\sim\dot\gamma$, or Bagnold scaling, $p\sim\dot\gamma^2$, depending on the details of the dissipation used. It is found that the onset of linear scaling is related to the appearance of force chains spanning the system. [Preview Abstract] |
Thursday, March 21, 2013 12:51PM - 1:03PM |
U29.00007: Relaxation time, viscosity and scaling at densities below jamming Peter Olsson We simulate soft-core bidisperse frictionless disks in two dimensions with overdamped dynamics at zero temperature and densities below jamming. We first prepare configurations by shearing at several constant shear rates $\dot\gamma$. These configurations are then used as starting points for simulations \emph{without} shearing that relax the system to zero energy. From these simulations we determine both the relaxation time, $\tau$, and the average path length traversed by the particles to reach the zero energy state. We find that $\tau$ diverges algebraically as a function of density, $\tau \sim (\phi_J-\phi)^{-\beta}$, if $\dot\gamma$ in the preparatory simulations is sufficiently small. We further find that the shear viscosity $\eta$ can be formally related to $\tau$, and that this gives a way to understand the origin of corrections to scaling in the scaling analysis of $\eta$[1]. The presence of the exponent $\beta+y$, where $y\approx 1.1$, in the scaling of the deviations from the $\dot\gamma\to0$ limit, $\eta(\phi,\dot\gamma)/ \eta(\phi,\dot\gamma\to0) = f((\phi_J-\phi)^{-(\beta+y)}\dot\gamma)$ [1], is also given an intuitive interpretation.\newline [1] P. Olsson and S. Teitel, Phys.\ Rev.\ E \textbf{83}, 030302(R), 2011. [Preview Abstract] |
Thursday, March 21, 2013 1:03PM - 1:15PM |
U29.00008: Shear shocks in fragile matter Vincenzo Vitelli, Stephan Ulrich, Nitin Upadhyaya Random media, like polymer networks, covalent network glasses, or grains under pressure can be viewed as elastic networks composed of springs and balls. The shear moduli of these types of materials typically vanish as the network connectivity $z$ approaches a critical value. In this talk, I show that shear strains propagate as diffusive fronts, whose {\bf width diverges} and whose {\bf transverse speed of sound vanishes}, as the transition is approached. Consequently, in this regime, linear theory breaks down, giving rise to {\bf nonlinear transverse waves}. Comparison of the analytical front profile to molecular dynamics simulations allows the extraction of the material constants of the network. Interestingly, even an {\bf undamped network} yields a {\bf diverging effective viscosity} caused by leaking of energy into non-affine degrees of freedom. [Preview Abstract] |
Thursday, March 21, 2013 1:15PM - 1:27PM |
U29.00009: Soft particle packings near jamming: correlations in static structure Kamran Karimi, Craig Maloney We extend our previous results report on 2D simulations of soft harmonic packings at various area fractions $\varphi $ above the jamming point $\varphi_{\mathrm{c}}$. We employ several statistical analyses to determine whether one or more characteristic lengths can be associated with either the quenched stress field in the packing or the structure of local elastic moduli. First, we define a locally anisotropic variant of the standard two-point correlation function. This anisotropic correlation function follows a power law even in globally isotropic stress states with a $\varphi $ independent exponent and no discernible cutoff within the statistically accessible regime. Secondly, we define a coarse-grained stress field on a scale R. The average anisotropic component and the fluctuations in the trace can both be collapsed onto similar master curves after rescaling R by a characteristic length scale $\xi $. $\xi $ accelerates as $\varphi $ approaches $\varphi_{\mathrm{c}}$, consistent with a divergence at $\varphi_{\mathrm{c}}$. Surprisingly, a similar analysis on the local coarse-grained elastic modulus tensor shows a non-trivial power-law scaling behavior as a function of the coarse-graining size yet no characteristic $\xi $ as exhibited by the stress. [Preview Abstract] |
Thursday, March 21, 2013 1:27PM - 1:39PM |
U29.00010: Elastic modulus of solid-like microsphere heaps Carlos Ortiz, Karen Daniels, Robert Riehn We study the elastic modulus of heaps of repulsive microspheres to gain insight into the nature of the rigidity of the material. The heaps are initially created by flowing a colloidal microsphere suspension towards a flat-topped ridge placed within a quasi two-dimensional microfluidic channel. The suspension flow-rate determines the heap size via the angle of repose. Using fluorescence video microscopy, we measure the fluorescent heap size until it reaches steady state. We directly visualize the elastic recoil of these steady state heaps in response to controlled changes in the fluid flow rate. We change the flow rate by an amount $\Delta v$ in a step-like fashion, and measure the amplitude of the bulk heap deformation $\Delta A$. We investigate both compressions and decompressions of varying amplitudes with respect to the steady state. Three deformation regimes are observed. No deformations are observed below a critical perturbation magnitude $\Delta v_c$. Above $\Delta v_c$, deformation amplitudes are linear with $\Delta v$. However, for large perturbations, nonlinear deformation amplitudes are observed, and their relationship is asymmetric with respect to compression and decompression. [Preview Abstract] |
Thursday, March 21, 2013 1:39PM - 1:51PM |
U29.00011: Investigating the stability of jammed systems with respect to generalized boundary deformations Samuel Schoenholz, Carl Goodrich, Oleg Kogan, Andrea Liu, Sidney Nagel At zero temperature and applied stress, amorphous packings of spheres exhibit a jamming transition as a function of packing fraction. Above the jamming transition, systems of repulsive spheres have a nonzero bulk moduli. However, some jammed states prepared with periodic boundary conditions are unstable to shear. These instabilities motivate several questions: How does the fraction of systems that exhibit instabilities scale with packing fraction and system size? Are there other classes of boundary deformations with respect to which jammed packings could be unstable, and if so, how can they be explored? We answer these questions by considering each finite packing with periodic boundary conditions in $d$ dimensions as the basis of an infinite hypercubic lattice. We study the properties of modes that do not respect the periodicity of the initial system and thereby characterize the linear response to a large class of boundary deformations. In this way we systematically explore the effects of system size and packing fraction on stability with respect to these boundary deformations, and show that our results can be understood in terms of competition between plane waves and anomalous vibrational modes associated with the jamming transition. [Preview Abstract] |
Thursday, March 21, 2013 1:51PM - 2:03PM |
U29.00012: Strong reduction of the rigidity of repulsive contact systems at vanishingly low temperatures Hajime Yoshino, Satoshi Okamura Contrarily to ordinary solids, the amorphous solid states of repulsive contact systems such as colloids and emulsions may not be regarded simply as harmonic states \footnote{C. F. Schreck,T. Bertrand, C. S. O'Hern, and M. D. Shattuck, Phys. Rev. Lett. 107, 078301 (2011).}. We studied the rigidity, i.~e. the shear-modulus of such a class of systems at vanishingly low but finite temperatures using the cloned liquid approach \footnote{H. Yoshino and M. M\'{e}zard, Phys. Rev. Lett. {\bf 105}, 015504 (2010), H. Yoshino, J. Chem. Phys. {\bf 136}, 214108 (2012), H. Yoshino, arXiv:1210.6826 (2012).} and molecular dynamic simulations. Our result implies breakdown of the commutation of the thermodynamic limit $N \to \infty$ and zero temperature limit $T \to 0$ for the response to shear: we found the rigidity in the limit $T \to 0$ is significantly smaller and exhibit a different scaling compared with that at $T=0$. Interestingly the rigidity in the limit $T \to 0$ exhibits the same scaling as the pressure, as observed experimentally in emulsions\footnote{T. G. Mason, J. Bibette and D. A. Weitz, Phys Rev. Lett. {\bf 75}, 2051 (1995)}. Detailed numerical examination suggests that the strong stress relaxation is due to contact opening events activated at vanishingly small temperatures. [Preview Abstract] |
Thursday, March 21, 2013 2:03PM - 2:15PM |
U29.00013: Mechanical instability at finite temperature Xiaoming Mao, Carlos I. Mendoza, Anton Souslov, Tom C. Lubensky Rigidity transitions have been well studied in a wide range of athermal systems such as jammed packings and diluted lattices, in which the balance between the number of degrees of freedom and constraints generally determines the onset of mechanical instability, as predicted by Maxwell. The effects of thermal fluctuations on these transitions, however, have not yet been systematically studied. Characterizing rigidity transitions at finite temperature is very important to the understanding of fundamental problems such as the relation between the glass transition and jamming. We report an analytic study of a finite-temperature rigidity transition in the square lattice. At zero temperature, this lattice exhibits a continuous transition between the square phase and a phase composed of rhombic cells as the nonlinear potential connecting next-nearest-neighbors vary. At nonzero-temperature, diverging vibrational entropy associated with the floppy modes play a very important role in selecting the phase and determining the order of the transition. We calculate the phase diagram of this system and identify interesting behaviors such as negative thermal expansion. [Preview Abstract] |
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