Local yield stress statistics in model amorphous solids

We develop and extend a method presented in [S. Patinet, D. Vandembroucq, and M. L. Falk, Phys. Rev. Lett., 117, 045501 (2016)] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a non-perturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process

Detailed analysis of the lattice Boltzmann method on unstructured grids

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.Comment: 42 page

Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method

Flow in porous media is a significant challenge to many computational fluid dynamics methods because of the complex boundaries separating pore fluid and host medium. However, the rapid development of the lattice Boltzmann methods and experimental imaging techniques now allow us to efficiently and robustly simulate flows in the pore space of porous rocks. Here we study the flow and dispersion in the pore space of limestone samples using the unstructured, characteristic based off-lattice Boltzmann method. We use the method to investigate the anomalous dispersion of particles in the pore space. We further show that the complex pore network limits the effectivity by which pollutants in the pore space can be removed by continuous flushing. In the smallest pores, diffusive transport dominates over advective transport and therefore cycles of flushing and no flushing, respectively, might be a more efficient strategy for pollutant removal

Non-Steady Wall-Bounded Flows of Viscoelastic Fluids Under Periodic Forcing

The problem of oscillating flows inside pipes under periodic forcing of viscoelastic fluids is addressed here. Starting from the linear Oldroyd-B model, a generalized Darcy's law is obtained in frequency domain and an explicit expression for the dependence of the dynamic permeability on fluid parameters and forcing frequency is derived. Previous results in both viscoelastic and Newtonian fluids are here shown to be particular cases of our results. On the basis of our calculations, a possible explanation for the observed damping of local dynamic response as the forcing frequency increases is given. Good fitting with recent experimental studies of wave propagation in viscoelastic media is here exhibited. Sound wave propagation in viscoelastic media flowing inside straight pipes is investigated. In particular, we obtain the local dynamic response for weakly compressible flows.Comment: 13 pages, 2 figure

Evaluation of the finite element lattice Boltzmann method for binary fluid flows

In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex boundaries. The current work combines characteristic-based integration of the streaming step with the free-energy based multiphase model by Lee et. al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for simulation time steps more than an order of magnitude larger than the relaxation time. Unlike previous work by Wardle et. al. [Computers and Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular forcing terms in the advection term, the current scheme applies collision and forcing terms locally for a simpler finite element formulation. A series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts.Comment: 26 page