Exact non-Hookean scaling of cylindrically bent elastic sheets and the large-amplitude pendulum

A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence on the interplate distance [Siber and Buljan, arXiv:1007.4699 (2010)]. The phenomenon has been used as a basis for an experimental problem at the 41st International Physics Olympiad. We show that the corresponding variational problem for the equilibrium energy of the deformed cylinder is equivalent to a minimum action description of a simple gravitational pendulum with an amplitude of 90 degrees. We use this analogy to show that the power-law of the force is exact for distances less than a critical value. An analytical solution for the elastic force is found and confirmed by measurements over a range of deformations covering both linear and non-Hookean behavior.Comment: 5 pages, extra figures and stability proof, accepted by American Journal of Physic

Deformation-induced accelerated dynamics in polymer glasses

Molecular dynamics simulations are used to investigate the effects of deformation on the segmental dynamics in an aging polymer glass. Individual particle trajectories are decomposed into a series of discontinuous hops, from which we obtain the full distribution of relaxation times and displacements under three deformation protocols: step stress (creep), step strain, and constant strain rate deformation. As in experiments, the dynamics can be accelerated by several orders of magnitude during deformation, and the history dependence is entirely erased during yield (mechanical rejuvenation). Aging can be explained as a result of the long tails in the relaxation time distribution of the glass, and similarly, mechanical rejuvenation is understood through the observed narrowing of this distribution during yield. Although the relaxation time distributions under deformation are highly protocol specific, in each case they may be described by a universal acceleration factor that depends only on the strain.Comment: 15 pages, 15 figure

Aging Effects Across the Metal-Insulator Transition in Two Dimensions

Aging effects in the relaxations of conductivity of a two-dimensional electron system in Si have been studied as a function of carrier density. They reveal an abrupt change in the nature of the glassy phase at the metal-insulator transition (MIT): (a) while full aging is observed in the insulating regime, there are significant departures from full aging on the metallic side of the MIT, before the glassy phase disappears completely at a higher density $n_g$; (b) the amplitude of the relaxations peaks just below the MIT, and it is strongly suppressed in the insulating phase. Other aspects of aging, including large non-Gaussian noise and similarities to spin glasses, also have been discussed.Comment: 4+ pages, 5 figures; minor changes, accepted for publication in PR

Simulations of aging and plastic deformation in polymer glasses

We study the effect of physical aging on the mechanical properties of a model polymer glass using molecular dynamics simulations. The creep compliance is determined simultaneously with the structural relaxation under a constant uniaxial load below yield at constant temperature. The model successfully captures universal features found experimentally in polymer glasses, including signatures of mechanical rejuvenation. We analyze microscopic relaxation timescales and show that they exhibit the same aging characteristics as the macroscopic creep compliance. In addition, our model indicates that the entire distribution of relaxation times scales identically with age. Despite large changes in mobility, we observe comparatively little structural change except for a weak logarithmic increase in the degree of short-range order that may be correlated to an observed decrease in aging with increasing load.Comment: 9 pages, 12 figure

Compressed correlation functions and fast aging dynamics in metallic glasses

We present x-ray photon correlation spectroscopy measurements of the atomic dynamics in a Zr67Ni33 metallic glass, well below its glass transition temperature. We find that the decay of the density fluctuations can be well described by compressed, thus faster than exponential, correlation functions which can be modeled by the well-known Kohlrausch-Williams-Watts function with a shape exponent {\beta} larger than one. This parameter is furthermore found to be independent of both waiting time and wave-vector, leading to the possibility to rescale all the correlation functions to a single master curve. The dynamics in the glassy state is additionally characterized by different aging regimes which persist in the deep glassy state. These features seem to be universal in metallic glasses and suggest a non diffusive nature of the dynamics. This universality is supported by the possibility of describing the fast increase of the structural relaxation time with waiting time using a unique model function, independently of the microscopic details of the system.Comment: 7 pages, 4 figures. To be published in J. Chem. Phy

Prediction of long and short time rheological behavior in soft glassy materials

We present an effective time approach to predict long and short time rheological behavior of soft glassy materials from experiments carried out over practical time scales. Effective time approach takes advantage of relaxation time dependence on aging time that allows time-aging time superposition even when aging occurs over the experimental timescales. Interestingly experiments on variety of soft materials demonstrate that the effective time approach successfully predicts superposition for diverse aging regimes ranging from sub-aging to hyper-aging behaviors. This approach can also be used to predict behavior of any response function in molecular as well as spin glasses.Comment: 13 pages, 4 figure

Subdiffusion and intermittent dynamic fluctuations in the aging regime of concentrated hard spheres

We study the nonequilibrium aging dynamics in a system of quasi-hard spheres at large density by means of computer simulations. We find that, after a sudden quench to large density, the relaxation time initially increases exponentially with the age of the system. After a surprisingly large crossover time, the system enters the asymptotic aging regime characterized by a linear increase of the relaxation time with age. In this aging regime, single particle motion is strongly non-Fickian, with a mean-squared displacement increasing subdiffusively, associated to broad, non-Gaussian tails in the distribution of particle displacements. We find that the system ages through temporally intermittent relaxation events, and a detailed finite size analysis of these collective dynamic fluctuations reveals that these events are not spanning the entire system, but remain spatially localized.Comment: 11 pages; 10 fig

Wrapping an adhesive sphere with a sheet

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss'Theorema Egregium shows that this operation necessarily generates metric distortions (i.e. stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two non-dimensional parameters comparing respectively bending and stretching energies to adhesion. A complete configuration diagram is finally proposed

Nonequilibrium Relaxations and Aging Effects in a Two-Dimensional Coulomb Glass

The relaxations of conductivity have been studied in the glassy regime of a strongly disordered two-dimensional electron system in Si after a temporary change of carrier density during the waiting time t_w. Two types of response have been observed: a) monotonic, where relaxations exhibit aging, i.e. dependence on history, determined by t_w and temperature; b) nonmonotonic, where a memory of the sample history is lost. The conditions that separate the two regimes have been also determined.Comment: 4 pages; published versioi

Interplay between shear loading and structural aging in a physical gel

We show that the aging of the mechanical relaxation of a gelatin gel exhibits the same scaling phenomenology as polymer and colloidal glasses. Besides, gelatin is known to exhibit logarithmic structural aging (stiffening). We find that stress accelerates this process. However, this effect is definitely irreducible to a mere age shift with respect to natural aging. We suggest that it is interpretable in terms of elastically-aided elementary (coil$\to$helix) local events whose dynamics gradually slows down as aging increases geometric frustration