This work proposes a model for granular deformation that predicts the stress and velocity profiles in well-developed dense granular flows. Recent models for granular elasticity (Jiang and Liu 2003) and rate-sensitive plastic flow (Jop et al. 2006) are reformulated and combined into one universal granular continuum law, capable of predicting flowing regions and stagnant zones simultaneously in any arbitrary 3D flow geometry. The unification is performed by justifying and implementing a Kroner-Lee elasto-plastic decomposition, with care taken to ensure certain continuum physical principles are necessarily upheld. The model is then numerically implemented in multiple geometries and results are compared to experiments and discrete simulations.
In this letter, we develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse grained quantities from simulations of dense disordered particulate systems, we present a coherent elasto-plastic model approach for deformation and flow of yield stress materials. For a given set of parameters, this model allows to match consistently transient and steady state features of driven disordered systems under both applied shear-rate and creep protocols.
The response of amorphous materials to an applied strain can be continuous, or instead display a macroscopic stress drop when a shear band nucleates. Such discontinuous response can be observed if the initial configuration is very stable. We study theoretically how such brittleness emerges in athermal, quasi-statically driven, materials as their initial stability is increased. We show that this emergence is well reproduced by elasto-plastic models and is predicted by a mean field approximation, where it corresponds to a continuous transition. In mean field, failure can be forecasted from the a…
Elastoplastic lattice models for the response of solids to deformation typically incorporate structure only implicitly via a local yield strain that is assigned to each site. However, the local yield strain can change in response to a nearby or even distant plastic event in the system. This interplay is key to understanding phenomena such as avalanches in which one plastic event can trigger another, leading to a cascade of events, but typically is neglected in elastoplastic models. To include the interplay one could calculate the local yield strain for a given particulate system and follow its…
Understanding the coupled thermo-mechanical behaviour of compacted granular beds can benefit various industrial applications, such as pebble bed design in fusion reactors. In this study, a thermo-mechanical discrete element method based on our previous work is improved and adapted to investigate the cyclic thermo-mechanical performance of gas-filled granular materials composed of elastoplastic grains. An interparticle contact model is developed considering the plastic deformation of grains. Through the simulation on a representative volume element of beryllium pebble beds, we provide grain-sca…
An elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. This paper discusses how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted or unique in the elastoplastic theories. An accurate condition of volume conservation is clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adop…
We simulate quasistatic flows of an ideal two-dimensional monodisperse foam around different obstacles, both symmetric and asymmetric, in a channel. We record both pressure and network contributions to the drag and lift forces, and study them as a function of obstacle geometry. We show that the drag force increases linearly with the cross section of an obstacles. The lift on an asymmetric aerofoil-like shape is negative and increases with its arc length, mainly due to the pressure contribution.
This work presents a new modeling approach to macroscopic, polycrystalline elasto-plasticity starting from first principles and a few well-defined structural assumptions, incorporating the mildly rate-dependent (viscous) nature of plastic flow and the microscopic origins of plastic deformations. For the global dynamics, we start from a two-stage time-stepping scheme, expressing the fact that in most real materials plastic flow is much slower than elastic deformations, and then perform a detailed analysis of the slow-loading limit passage. In this limit, a rate-independent evolution can be expe…
In this paper we present a new general framework for anisotropic elastoplasticity at large strains. The new framework presents the following characteristics: (1) It is valid for non-moderate large strains, (2) it is valid for both elastic and plastic anisotropy, (3) its description in rate form is parallel to that of the infinitesimal formulation, (4) it is compatible with the multiplicative decomposition, (5) results in a similar framework in any stress-strain work-conjugate pair, (6) it is consistent with the principle of maximum plastic dissipation and (7) does not impose any restriction on…
Elasto-plastic models are among the most successful ways to study the critical properties of the plastic yielding transition of amorphous solids. Typically these models are studied under a condition of constant transition rates from one plastic configuration to another, and in this form they predict the existence of well defined critical exponents that display universality, in the same sense that in standard equilibrium phase transitions. I show however that very naturally the transition rates must not be taken as a constant, but dependent of the local stress excess above the critical value. T…
The complex incremental behavior of granular materials is explored with multi-directional loading probes. An advanced discrete element model (DEM) was used to examine the reversible and irreversible strains for small loading probes, which follow an initial monotonic axisymmetric triaxial loading. The model used non-convex non-spherical particles and an exact implementation of the Hertz-like Cattaneo-Mindlin model for the contact interactions. Rectilinear true-triaxial probes were used in the study (i.e., no direct shear strain or principal stress rotation), with small strains increments of $2\…
Creep mechanisms in uniaxially compressed 3D granular solids comprised of faceted frictionless grains are studied numerically using a constant pressure and constant stress simulation method. Rapid uniaxial compression followed by slow dilation is predicted on the basis of a logarithmic creep phenomenon. Micromechanical analysis indicates the existence of a correlation between granular creep and grain-scale deformations. Localized regions of large strain appear during creep and grow in magnitude and size with time. Furthermore, the accumulation of non-affine granular displacements increases lin…
We study the response of F-actin bundles to driving forces through a simple analytical model. We consider two filaments connected by reversibly bound crosslinks and driven by an external force. Two failure modes under load can be defined. \textit{Brittle failure} is observed when crosslinks suddenly and collectively unbind, leading to catastrophic loss of bundle integrity. During \textit{ductile failure}, on the other hand, bundle integrity is maintained, however at the cost of crosslink reorganization and defect formation. We present phase diagrams for the onset of failure, highlighting the i…
Upon loading, amorphous solids can exhibit brittle yielding, with the abrupt formation of macroscopic shear bands leading to fracture, or ductile yielding, with a multitude of plastic events leading to homogeneous flow. It has been recently proposed, and subsequently questioned, that the two regimes are separated by a sharp critical point, as a function of some control parameter characterizing the intrinsic disorder strength and the degree of stability of the solid. In order to resolve this issue, we have performed extensive numerical simulations of athermally driven elasto-plastic models with…
We present an experimental study of the deformation inside a granular material that is progressively tilted. We investigate the deformation before the avalanche with a spatially resolved Diffusive Wave Spectroscopy setup. At the beginning of the inclination process, we first observe localized and isolated events in the bulk, with a density which decreases with the depth. As the angle of inclination increases, series of micro-failures occur periodically in the bulk, and finally a granular avalanche takes place. The micro-failures are observed only when the tilt angles are larger than a threshol…
Granular packings under constant shear stress display below the Coulomb limit, a logarithmic creep dynamics. However the addition of small stress modulations induces a linear creep regime characterized by an effective viscous response. Using Diffusing Wave Spectroscopy, we investigate the relation between creep and local plastic events spatial distribution ("hot-spots") contributing to the plastic yield. The study is done in the two regimes, i.e. with and without mechanical activation. The hot-spot dynamics is related to the material effective fluidity. We show that far from the threshold, a l…
The phenomenon of crumpling is common in our daily life and nature. It exhibits many interesting properties, such as ultra-tough resistance to pressure with less than 30$\%$ of volume density, power-law relation for pressure vs density, and crackling noises with occurrence frequency vs intensity mimicking that of earthquakes. These results are mainly obtained by using flat thin sheets. But, in reality the majority of crumpled objects exhibit nonzero intrinsic curvatures. Notable examples are crushed aluminum cans, car wreckage, and cells move in and out of blood vessels. In this work we concen…
We present generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength. The proposed mechanistic contact laws are continuous at the onset of unloading by means of a regularization term, in the spirit of a cohesive zone model, that introduces a small and controllable error in the conditions for interparticle breakage. This continuity property is in sharp contrast with the behavior of standard mechanistic loading and unloading contact theories, which exhibit a discontinuity at the onset of unloading when particles form solid bridges during plastic deformation. The…
Accounting for elasto-plastic motion in granular media, hypoplasticity is a state-of-the-art constitutive model derived from data accumulated over many decades. In contrast, GSH, a hydrodynamic theory, is derived from general principles of physics, with comparatively few inputs from experiments, yet sporting an applicability ranging from static stress distribution via elasto-plastic motion to fast dense flow, including non-uniform ones such as a shear band. Comparing both theories, we find great similarities for uniform, slow, elasto-plastic motion. We also find that proportional paths and the…
Propotional paths as summed up by the Goldscheider Rule (GR) -- stating that given a constant strain rate, the evolution of the stress maintains the ratios of its components -- is a characteristics of elasto-plastic motion in granular media. Barodesy, a constitutive relation proposed recently by Kolymbas, is a model that, with GR as input, successfully accounts for data from soil mechanical experiments. Granular solid hydrodynamics (GSH), a theory derived from general principles of physics and two assumptions about the basic behavior of granular media, is constructed to qualitatively account f…
We report a combined experimental and simulation study of deformation-induced diffusion in compacted two-dimensional amorphous granular pillars, in which thermal fluctuations play negligible role. The pillars, consisting of bidisperse cylindrical acetal plastic particles standing upright on a substrate, are deformed uniaxially and quasistatically by a rigid bar moving at a constant speed. The plastic flow and particle rearrangements in the pillars are characterized by computing the best-fit affine transformation strain and non-affine displacement associated with each particle between two stage…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of 'mesoscopic' blocks alternating between an elastic behavior and plastic relaxation, when they are too loaded. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. We review not only the physical insight provided by these models into practical issues such as strain…
Non-linear visco-elasto-plastic rheology of a viscous vertex model
Aix Marseille Univ, Université de Toulon, CNRS, CPT (UMR 7332), Turing Centre for Living systems（艾克斯-马赛大学，土伦大学，法国国家科学研究中心，理论物理与粒子物理中心（UMR 7332），图灵生命系统中心）；Institut für Theoretische Physik, Universität Innsbruck（因斯布鲁克大学理论物理研究所）
We identify the sequence of microstructural changes that characterize the evolution of an attractive particulate gel under flow and discuss their implications on macroscopic rheology. Dissipative Particle Dynamics (DPD) is used to monitor shear-driven evolution of a fabric tensor constructed from the ensemble spatial configuration of individual attractive constituents within the gel. By decomposing this tensor into isotropic and non-isotropic components we show that the average coordination number correlates directly with the flow curve of the shear stress vs. shear rate, consistent with theor…
Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline, polycrystalline and other materials --- feature a predominantly elastic response at small stresses, plasticity onset at a rather well-defined yield stress and rate-dependence. Necking instabilities involve a unique coupling between the system's geometry and its constitutive behavior. We consider generic elasto-viscoplastic constitutive relations involving an i…
Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for micr…
Electrostatic theory preserves charges, but allows dipolar excitations. Elasticity theory preserves dipoles, but allows quadrupolar (Eshelby like) plastic events. Charged amorphous granular systems are interesting in their own right; here we focus on their plastic instabilities and examine their mechanical response to external strain and to external electric field, to expose the competition between elasticity and electrostatics. In this paper a generic model is offered, its mechanical instabilities are examined and a theoretical analysis is presented. Plastic instabilities are discussed as sad…
Plastic yield of amorphous solids occurs by power law distributed slip avalanches whose universality is still debated. Determination of the power law exponents from experiments and molecular dynamics simulations is hampered by limited statistical sampling. On the other hand, while existing elasto-plastic depinning models give precise exponent values, these models to date have been limited to a scalar approximation of plasticity which is difficult to reconcile with the statistical isotropy of amorphous materials. Here we introduce for the first time a fully tensorial mesoscale model for the ela…
The granular silo is one of the many interesting illustrations of the thixotropic property of granular matter: a rapid flow develops at the outlet, propagating upwards through a dense shear flow while material at the bottom corners of the container remains static. For large enough outlets, the discharge flow is continuous; however, by contrast with the clepsydra for which the flow velocity depends on the height of fluid left in the container, the discharge rate of granular silos is constant. Implementing a plastic rheology in a 2D Navier-Stokes solver (following the mu(I)-rheology or a constan…
Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to a vanishing of a real eigenvalue of the Hessian matrix, frictional granular materials can exhibit a previously unnoticed additional mechanism for instabilities, i.e. the appearance of a pair of complex eigenvalues leading to oscillatory exponential growth of perturbations which are tamed by dynamical nonlinearities. This fundamental difference appears crucial for the …
Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic mode…
