Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids

We use the shear transformation zone (STZ) theory of dynamic plasticity to study the necking instability in a two-dimensional strip of amorphous solid. Our Eulerian description of large-scale deformation allows us to follow the instability far into the nonlinear regime. We find a strong rate dependence; the higher the applied strain rate, the further the strip extends before the onset of instability. The material hardens outside the necking region, but the description of plastic flow within the neck is distinctly different from that of conventional time-independent theories of plasticity.Comment: 4 pages, 3 figures (eps), revtex4, added references, changed and added content, resubmitted to PR

Rate dependent shear bands in a shear transformation zone model of amorphous solids

We use Shear Transformation Zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts homogeneous deformation for shorter quench times and lower strain rates, and inhomogeneous deformation for longer quench times and higher strain rates. The location of the transition between homogeneous and inhomogeneous flow on the deformation map is determined in part by the steady state effective temperature, which is likely material dependent. This model also suggests that material failure occurs due to a runaway feedback between shear heating and the local disorder, and provides an explanation for the thickness of shear bands near the onset of material failure. We find that this model, which resolves dynamics within a sheared material interface, predicts that the stress weakens with strain much more rapidly than a similar model which uses a single state variable to specify internal dynamics on the interface.Comment: 10 pages, 13 figures, corrected typos, added section on rate strengthening vs. rate weakening material

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

Young red supergiants and the near infrared light appearance of disk galaxies

Disk galaxies often show prominent nonaxisymmetric features at near-infrared wavelengths. Such features may indicate variations in the surface density of stellar mass, contributions from young red supergiants in star forming regions, or substantial dust obscuration. To distinguish among these possibilities, we have searched for spatial variations in the 2.3 micron photometric CO index within the disks of three nearby galaxies (NGC 278, NGC 2649, & NGC 5713). This index measures the strength of the absorption bands of molecular CO in stellar atmospheres, and is strong in cool, low surface-gravity stars, reaching the largest values for red supergiants. We observe significant spatial CO index variations in two galaxies (NGC 278 & NGC 5713), indicating that the dominant stellar population in the near-infrared is not everywhere the same. Central CO index peaks are present in two galaxies; these could be due to either metallicity gradients or recent star formation activity. In addition, significant azimuthal CO index variations are seen in NGC 278. Because strong azimuthal metallicity gradients are physically implausible in disk galaxies, these features are most naturally explained by the presence of a young stellar population. The fraction of 2 micron light due to young stellar populations in star forming regions can be calculated from our data. Overall, young stellar populations can contribute ~3% of a (normal) galaxy's near infrared flux. Locally, this fraction may rise to ~33%. Thus, young stars do not dominate the total near infrared flux, but can be locally dominant in star forming regions, and can bias estimates of spiral arm amplitude or other nonaxisymmetric structures in galaxies' mass distributions.Comment: 28 pages including 3 postscript figures. A fourth figure is in jpeg format. Uses AASTeX. Accepted for publication in The Astronomical Journa

Metastability in Two Dimensions and the Effective Potential

We study analytically and numerically the decay of a metastable phase in (2+1)-dimensional classical scalar field theory coupled to a heat bath, which is equivalent to two-dimensional Euclidean quantum field theory at zero temperature. By a numerical simulation we obtain the nucleation barrier as a function of the parameters of the potential, and compare it to the theoretical prediction from the bounce (critical bubble) calculation. We find the nucleation barrier to be accurately predicted by theory using the bounce configuration obtained from the tree-level (``classical'') effective action. Within the range of parameters probed, we found that using the bounce derived from the one-loop effective action requires an unnaturally large prefactor to match the lattice results. Deviations from the tree-level prediction are seen in the regime where loop corrections would be expected to become important.Comment: 13pp, LaTex with Postscript figs, CLNS 93/1202, DART-HEP-93/0

Dynamics and Thermodynamics of the Glass Transition

The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with A. Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature $T_K$. This partially broken ergodicity seems to explain the vanishing entropy at $T_K$ and other observed relations between dynamics and thermodynamics at the glass transition.Comment: 20 pages, no figures, some further revision