Amorphous solids are ubiquitous among natural and man-made materials. Often used as structural materials for their attractive mechanical properties, their utility depends critically on their response to applied stresses. Processes underlying such mechanical response, and in particular the yielding behaviour of amorphous solids, are not satisfactorily understood. Although studied extensively, observed yielding behaviour can be gradual and depend significantly on conditions of study, making it difficult to convincingly validate existing theoretical descriptions of a sharp yielding transition. Here we employ oscillatory deformation as a reliable probe of the yielding transition. Through extensive computer simulations for a wide range of system sizes, we demonstrate that cyclically deformed model glasses exhibit a sharply defined yielding transition with characteristics that are independent of preparation history. In contrast to prevailing expectations, the statistics of avalanches reveals no signature of the impending transition, but exhibit dramatic, qualitative, changes in character across the transition.

We compare predictions from two familiar models of the metastable supercooled liquid respectively constructed with thermodynamic and dynamic approach. In the so called density functional theory (DFT) the free energy F [ρ] of the liquid is a functional of the inhomogeneous density ρ(r).The metastable state is identified as a local minimum of F [ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-nonergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained respectively in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes. 0

We present a numerical investigation of the density fluctuations in a model glass under cyclic shear deformation conditions. We demonstrate that in our model glass, the compressibility is suppressed in inherently minimally energetic structures, showing a hyperuniform trend at a density which is below the critical jamming density. At low shear amplitudes, i.e. below the yield amplitude, the system reaches an absorbent steady state in which density fluctuations are suppressed, revealing the clear fingerprint of hyperuniformity up to a finite length scale. The opposite scenario is observed above the yield amplitude, where density fluctuations are strongly enhanced. We demonstrate that the transition to this state is accompanied by a spatial phase separation into two distinct hyperuniform regions, as a consequence of shear band formation at amplitudes greater than the yield amplitude.

Using the time dependence of density fluctuations in a supercooled liquid obtained from the solutions of the equations of nonlinear fluctuating hydrodynamics (NFH), the evolution of the system in the free energy landscape is studied. A crossover from a continuous fluid type dynamics to that of hopping between different free energy minima is observed as the liquid is increasingly supercooled. We demonstrate that our results are also in agreement with equilibrium density functional analysis of the same system. The density field obtained in the numerical solution of the NFH equations are further analyzed to introduce complimentary density of voids in the supercooled liquid state and its static and dynamic correlations are computed. The nature of the relaxation of vacancy correlations are observed to be similar to that of the density fluctuations.

The free energy of a hard-sphere fluid for which the average energy is trivial signifies how its entropy changes with packing. The packing η_{f} at which the free energy of the crystalline state becomes lower than that of the disordered fluid state marks the freezing point. For packing fractions η>η_{f} of the hard-sphere fluid, we use the modified weighted density functional approximation to identify metastable free energy minima intermediate between uniform fluid and crystalline states. The distribution of the sharply localized density profiles, i.e., the inhomogeneous density field ρ(x) characterizing the metastable state is primarily described by a pair function g_{s}(η/η_{0}). η_{0} is a structural parameter such that for η=η_{0} the pair function is identical to that for the Bernal random structure. The configurational entropy S_{c} of the metastable hard-sphere fluid is calculated by subtracting the corresponding vibrational entropy from the total entropy. The extrapolated S_{c} vanishes as η→η_{K} and η_{K} is in agreement with other works. The dependence of η_{K} on the structural parameter η_{0} is obtained.