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Register a new userCorrelation and shear bands in a plastically deformed granular medium
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Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic model of solid flow that incorporates a local Mohr-Coulomb failure criterion. We show that the angle observed in the microscopic correlations can be understood by combining the elastic interactions associated with Eshelby transformation with the local failure criterion. At large strains, we also induce permanent shear bands at an angle that is different from the one observed in the correlation pattern. We interpret this angle as the one that leads to the maximal instability of slip lines.
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How does pore liquid reconfigure within shear bands in wet granular media? Conventional wisdom predicts that liquid is drawn into dilating granular media. We, however, find a depletion of liquid in shear bands despite increased porosity due to dilatancy. This apparent paradox is resolved by a microscale model for liquid transport at low liquid contents induced by rupture and reconfiguration of individual liquid bridges. Measured liquid content profiles show macroscopic depletion bands similar to results of numerical simulations. We derive a modified diffusion description for rupture-induced liquid migration.
We report on experiments that probe the stability of a two-dimensional jammed granular system formed by imposing a quasistatic simple shear strain $gamma_{rm I}$ on an initially stress free packing. We subject the shear jammed system to quasistatic cyclic shear with strain amplitude $deltagamma$. We observe two distinct outcomes after thousands of shear cycles. For small $gamma_{rm I}$ or large $deltagamma$, the system reaches a stress-free, yielding state exhibiting diffusive strobed particle displacements with a diffusion coefficient proportional to $deltagamma$. For large $gamma_{rm I}$ and small $deltagamma$, the system evolves to a stable state in which both particle positions and contact forces are unchanged after each cycle and the response to small strain reversals is highly elastic. Compared to the original shear jammed state, a stable state reached after many cycles has a smaller stress anisotropy, a much higher shear stiffness, and less tendency to dilate when sheared. Remarkably, we find that stable states show a power-law relation between shear modulus and pressure with an exponent $betaapprox 0.5$, independent of $deltagamma$. Based on our measurements, we construct a phase diagram in the $(gamma_{rm I},deltagamma)$ plane showing where our shear-jammed granular materials either stabilize or yield in the long-time limit.
We analyse the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strainrates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strainrate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in compressional direction and propagate in dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.
The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach: irreversible, plastic deformation of single crystals. We show for the superconductor SrTiO$_3$ that compressive plastic deformation induces low-dimensional superconductivity significantly above the superconducting transition temperature ($T_c$) of undeformed samples, with evidence of superconducting correlations at temperatures two orders of magnitude above the bulk $T_c$. The superconductivity enhancement is correlated with the appearance of self-organized dislocation structures, as revealed by diffuse neutron and X-ray scattering. We also observe signatures of deformation-induced quantum-critical ferroelectric fluctuations and inhomogeneous ferroelectric order via Raman scattering. These results suggest that the strain surrounding the self-organized dislocation structures induces local ferroelectricity and quantum-critical dynamics that strongly influence $T_c$, consistent with a theory of superconductivity enhanced by soft polar fluctuations. More broadly, our results demonstrate the promise of plastic deformation and dislocation engineering as tools to manipulate electronic properties of quantum materials.
Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion leaving adjacent regions essentially rigid[1,2,3,4,5]. Since shear bands mark areas of flow, material failure and energy dissipation, they play a crucial role for many industrial, civil engineering and geophysical processes[6]. They also appear in related contexts, such as in lubricating fluids confined to ultra-thin molecular layers[7]. Detailed information on motion within a shear band in a three-dimensional geometry, including the degree of particle rotation and inter-particle slip, is lacking. Similarly, only little is known about how properties of the individual grains - their microstructure - affect movement in densely packed material[5]. Combining magnetic resonance imaging, x-ray tomography, and high-speed video particle tracking, we obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.
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