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 study the yielding behaviour of a model glass under cyclic athermal quastistatic deformation computationally, and show that yielding is characterised by the discontinuous appearance of shear bands, whose width is about ten particle diameters at their initiation, in which the strain gets localised. Strain localisation is accompanied by a corresponding change in the energies, and a decrease in the density in the shear band. We show that the glass remains well annealed outside the shear band whereas the energies correspond to the highest possible energy minima at the given density within the shear band. Diffusive motion of particles characterising the yielded state are confined to the shear bands, whose mean positions display movement over repeated cycles. Outside the shear band, particle motions are sub-diffusive but remain finite. Despite the discontinuous nature of their appearance, shear bands are reversible in the sense that a reduction in the amplitude of cyclic deformation to values below yielding leads to the healing and disappearance of the shear bands.The mechanical response of amorphous solids to applied stresses is of obvious importance in characterising their behaviour. Beyond the elastic regime at small applied stresses, such response is characterised by plastic deformations, and beyond yielding, by flow. Considerations associated with yielding are of relevance to a wide range of phenomena, from irreversible deformation and failure in atomic and molecular glasses, such as metallic glasses, to the complex rheology of soft materials such as foams, emulsions, colloidal suspensions, and granular matter [1][2][3][4][5]. Although yielding and flow may apparently be continuous and homogeneous for some yield stress fluids, it is a sharp, discontinuous event at the other end of the spectrum, as in brittle failure, characterised by localisation of strain and the formation of shear bands. Systems and questions of interest range from the mechanical properties of nanostructures to large scale phenomena such as mud-slides and earthquakes [6][7][8][9]. Viewed as a nonequilibrium transition in a driven system, the phenomena associated with yielding have in recent years been investigated in a large number of studies experimentally, through computer simulations, and the analysis of elastoplastic and other models . Many studies have focussed on the anisotropic interactions arising between localised plastic events or STZs [17,[33][34][35][36][37][38], and, in particular, how they may influence strain localisation. Yielding has been analysed through the application of STZ theory [3,14], described as a critical transition in analogy with depinning of manifolds in random media [13,19], a discontinuous transition associated with a spionodal [28,29], etc., and the relationship between these descriptions is a subject of ongoing investigations (e. g., [31,32]). The role of the degree of annealing in determining the nature of the yielding transition, and in the formation and character of shear bands, has increasingly been appr...

The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its the thermodynamics via. the configurational entropy, and is of fundamental importance in descriptions of glassy behaviour. The breakdown of the Stokes-Einstein (SEB) relation between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.It is now clear from extensive research over the last two decades that, as a liquid is gradually (super)cooled, its dynamics becomes spatially heterogeneous ("dynamical heterogeneity") [1][2][3] and the collective nature of the underlying relaxation processes can be quantified by various growing correlation length scales [4, 5]. Dynamics can be described by different measures -the translational diffusion coefficient (D), the shear viscosity (η) or the α-relaxation time (τ α ). At high temperatures, where particle motions are diffusive, all these time scales are mutually coupled. D and η are related via the Stokes-Einstein (SE) relation [6, 7] : D = mk B cπ T Rη , (m, R are respectively mass and radius of a diffusing particle, T is the temperature of the liquid and the constant c depends on stick or slip boundary condition). At high temperatures, owing to exponential decay of self-intermediate scattering function F s (k, t) = exp(−Dk 2 t) at all probe wave vectors k, D also gets coupled to the relaxation time τ (k) measured from F s (k, t) : Dk 2 τ (k) = constant. Further, τ α is often used as a proxy for η (or η/T ) in the SE relation to save computational cost. At low temperatures in dense, viscous liquids, D becomes much bigger than the value estimated from τ α (η) using the SE relation. This phenomenon is known as the breakdown of the SE relation (SEB) [2,[8][9][10][11][12][13] [1, 2, 7, 8] interprets the SEB as a consequence of the dynamical heterogeneity (DH) developing in the liquid upon cooling. DH simply means that there are populations of slow and fast particles which form transient clusters, making the dynamics spatially heterogeneous. The existence of DH leads to the expectation of a distribution of diffusion coefficients and relaxation times [12,14] corresponding to populations of different mobility. The observed D is dominated by the fast population, while the observed τ (or η) is governed mainly by the slow population, leading to the decoupling and the SEB. The observed decoupling (SEB) is an average effect in such a picture, which however, does not clarify the role played by a heterogeneity length scale.The breakdown of the SE relation poses a puzzle...