On the Bauschinger effect in supercoooled melts under shear: results from mode coupling theory and molecular dynamics simulations

We study the nonlinear rheology of a glass-forming binary mixture under the reversal of shear flow using molecular dynamics simulations and a schematic model of the mode-coupling theory of the glass transition (MCT). Memory effects lead to a history-dependent response, as exemplified by the vanishing of a stress-overshoot phenomenon in the stress--strain curves of the sheared liquid, and a change in the apparent elastic coefficients around states with zero stress. We investigate the various retarded contributions to the stress response at a given time schematically within MCT. The connection of this macroscopic response to single-particle motion is demonstrated using molecular-dynamics simulation

Nonlinear response of glass–forming dispersions under applied time–dependent deformations

In this thesis, I have discussed the nonlinear response of glass–forming dispersions under applied time–dependent deformations. This topic provides insight in the dynamics of such materials close to the glass transition. The nonlinear response offers a further comprehension of the glass transition and the nature of the glass. I have described the process of yielding as a transition from the anelastic stress response to plastic flow and as a transition from a deformed to a shear–melted glass. The schematic MCT model, which I have used to describe the response to time–dependent shear flow and to applied stress, gives the transient time–dependence of the response. By omitting the wave–vector dependence, I have lost structural information. I can interpret the structural dynamics only in the context of the microscopic MCT theory, by relating the density correlation function of the schematic model to the corresponding correlation functions of the microscopic theory.By an instantaneous change of direction of the imposed shear flow, I have studied the history–dependent response of materials in proximity of the glass transition. In equilibrium physics, a change in the observables can be explained by a change of the variables defining each state. The schematic MCT model obtains a nonequilibrium observable by taking the whole deformation history into account, based on the ITT–MCT approach [10].Using this history–dependence of the response to a shear reversal, I have probed the dynamics at the time of the reversal. I have rationalized the phenomena of residual strains, decreased overshoots and a softer apparent elasticity as results of stress contributions of the preshear, the shear flow before the reversal of its direction. By systematic computations of the quantifying observables of these phenomena for preshear strains from zero to one, I have discussed the effect of the yielding transition on the preshear dependence. This discussion is consistent, with the interpretation of the yielding as the transition from a (mostly) reversible anelastic regime to the steady state of irreversible flow.The density–dependence of the elasticity of the quiescent glass and the shear–rate dependence of transient stress overshoots and steady states persists in the results for a shear–flow reversal. I have traced the scaling with the separation parameter, that corresponds to a relative density, back to the scaling of the nonergodicity parameter.Using the numerical inversion of the schematic MCT model, I have computed the strain response under applied constant stress, known as creep. The inversion simplifies the analysis of the relation between strain–controlled and stress–controlled rheology. In the linear response regime, for both stress steps and stress ramps, I have connected every increase of the strainto a known dissipative process in the glass. The onset of the nonlinear response depends in my computations on the same mechanisms related to the yielding of a glass under steady shear.I can rule out for the schematic MCT model, that asymptotic flow is caused by an applied stress smaller than the dynamical yield stress. Any applied stress larger than the yield stress results in asymptotic flow. I have introduced a schematic overview, which separates glassy from fluid dynamics and linear from nonlinear response. The yielding transition is connected to the transition from linear to nonlinear response of the glass.The results for the stress response after a shear–flow reversal and for strain response under applied stress show new aspects on the onset of nonlinear response. Stress and stain response can be described by the same fundamental principles. In this work, the process of homogeneous yielding is attributed to a collective cage breaking of neighboring particles, represented in ITT–MCT by a dephasing of the derivatives of the static structure factor [41].To advance the discussion of the transient time dependence of yielding, the underlying structural mechanisms should be studied in the microscopic MCT and in Brownian dynamics simulations

Rheology of Inelastic Hard Spheres at Finite Density and Shear Rate

Considering a granular fluid of inelastic smooth hard spheres, we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress sigma to the shear rate gamma and predictions of the yield stress complete our discussion of granular rheology derived from first principles

Integration through transients for inelastic hard sphere fluids

We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalize the Integration Through Transients formalism to a fluid of dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory-based on the physical picture that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signaled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of epsilon, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity

Nonlinear mechanical response of supercooled melts under applied forces

We review recent progress on a microscopic theoretical approach to describe the nonlinear response of glass-forming colloidal dispersions under strong external forcing leading to homogeneous and inhomogeneous flow. Using mode-coupling theory (MCT), constitutive equations for the rheology of viscoelastic shear-thinning fluids are obtained. These are, in suitably simplified form, employed in continuum fluid dynamics, solved by a hybrid-Lattice Boltzmann (LB) algorithm that was developed to deal with long-lasting memory effects. The combined microscopic theoretical and mesoscopic numerical approach captures a number of phenomena far from equilibrium, including the yielding of metastable states, process-dependent mechanical properties, and inhomogeneous pressure-driven channel flow