Spatiotemporal correlations between plastic events in the shear flow of athermal amorphous solids

The slow flow of amorphous solids exhibits striking heterogeneities: swift localised particle rearrangements take place in the midst of a more or less homogeneously deforming medium. Recently, experimental as well as numerical work has revealed spatial correlations between these flow heterogeneities. Here, we use molecular dynamics (MD) simulations to characterise the rearrangements and systematically probe their correlations both in time and in space. In particular, these correlations display a four-fold azimuthal symmetry characteristic of shear stress redistribution in an elastic medium and we unambiguously detect their increase in range with time. With increasing shear rate, correlations become shorter-ranged and more isotropic. In addition, we study a coarse-grained model motivated by the observed flow characteristics and challenge its predictions directly with the MD simulations. While the model captures both macroscopic and local properties rather satisfactorily, the agreement with respect to the spatiotemporal correlations is at most qualitative. The discrepancies provide important insight into relevant physics that is missing in all related coarse-grained models that have been developed for the flow of amorphous materials so far, namely the finite shear wave velocity and the impact of elastic heterogeneities on stress redistribution

Effects of inertia on the steady-shear rheology of disordered solids

We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping magnitude $\zeta$ in the low-temperature limit, we identify two well defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number $Wi= \zeta \dot\gamma$ (up to elastic parameters); the macroscopic stress $\Sigma$ follows the frequently encountered Herschel-Bulkley law $\Sigma= \Sigma\_0 + k \sqrt{Wi}$, with yield stress \Sigma\_0\textgreater{}0. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes non-monotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably due to, and in proportion to, the driving. By suitably thermostatting more or less underdamped systems, we show that their rheology only depends on their kinetic temperature and the shear rate, rescaled with Einstein's vibration frequency.Comment: Accepted for publication in Phys. Rev. Let

Free energy functionals for efficient phase field crystal modeling of structural phase transformations

The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory (CDFT), but its single mode free energy functional only leads to lattices with triangular (2D) or BCC (3D) symmetries. By returning to a closer approximation of the CDFT free energy functional, we develop a systematic construction of two-particle direct correlation functions that allow the study of a broad class of crystalline structures. This construction examines planar spacings, lattice symmetries, planar atomic densities and the atomic vibrational amplitude in the unit cell of the lattice and also provides control parameters for temperature and anisotropic surface energies. The power of this new approach is demonstrated by two examples of structural phase transformations.Comment: 4 pages, 4 figure