Understanding the relationship between micromechanics and macroscopic plastic deformation is vital for elucidating the deformation mechanism of amorphous solids, such as granular materials. In this study, we directly measure T1 events, which are topological rearrangements of particles, and the associated microscopic stresses in dense packings of photoelastic disks under pure shear. We observe a remarkable similarity between the evolution of the total number of T1 events and the global stress-strain curve. The competition between the birth and death of T1 events establishes a dynamic equilibrium after the yield strain, contributing to the overall plastic behavior. Despite the erratic stress fluctuations of individual T1 events, the local stresses decrease on average once T1 events occur, indicating their soft characteristics. Furthermore, we demonstrate that the microscopic stress fluctuations exhibit a long-range anisotropic spatial correlation similar to the Eschelby character, but with a distinct scaling of $r^{-1.5}$. Interestingly, we also find a striking similarity in the correlation functions of T1 and non-T1 regions. These findings establish a significant connection between macroscopic mechanical behavior and the elementary deformation of T1 events, shedding light on the fundamental understanding of granular materials as amorphous solids with contact-scale plastic deformation.
The mechanical properties of a disordered heterogeneous medium depend, in general, on a complex interplay between multiple length scales. Connecting local interactions to macroscopic observables, such as stiffness or fracture, is thus challenging in this type of material. Here, we study the properties of a cohesive granular material composed of glass beads held together by soft polymer bridges. We characterise the mechanical response of single bridges under traction and shear, using a setup based on the deflection of flexible micropipettes. These measurements, along with information from X-ray…
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…
Biot's theory predicts the wave velocities of a saturated poroelastic granular medium from the elastic properties, density and geometry of its dry solid matrix and the pore fluid, neglecting the interaction between constituent particles and local flow. However, when the frequencies become high and the wavelengths comparable with particle size, the details of the microstructure start to play an important role. Here, a novel hydro-micromechanical numerical model is proposed by coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM. The model allows to investigate the d…
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 behavior of granular media under quasi-static loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regim…
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…
When an amorphous material is strained beyond the point of yielding it enters a state of continual reconfiguration via dissipative, avalanche-like slip events that relieve built-up local stress. However, how the statistics of such events depend on local interactions among the constituent units remains debated. To address this we perform experiments on granular material in which we use particle shape to vary the interactions systematically. Granular material, confined under constant pressure boundary conditions, is uniaxially compressed while stress is measured and internal rearrangements are 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…
In both nature and engineering, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We use the discrete element method to investigate the stress distribution developed within the granular packing as a result of compaction due to the displacement of a rigid piston. We observe that the stress within the packing increases exponentially with the length of accumulated grains, and show an extension to current analytic models which fits the measured st…
We analyze the isotropic compaction of assemblies composed of soft pentagons interacting through classical Coulomb friction via numerical simulations. The effect of the initial particle shape is discussed by comparing packings of pentagons with packings of soft circular particles. We characterize the evolution of the packing fraction, the elastic modulus, and the microstructure (particle rearrangement, connectivity, contact force and particle stress distributions) as a function of the applied stresses. Both systems behave similarly; the packing fraction increases and tends asymptotically to a …
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\…
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…
This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to $1$, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increase…
Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stress-strain relation for a plastic flow rule is derived. The fluctuations account for non-associativity in plastic deformations typically observed in heterogeneous materials. Second, an axisymmetric spherical shell compaction model is extended to account for fluctuations in the material microstructure due to granular interactions at the pore scale. This changes the stress-strain constitutive equation determining the dynamics of pore collapse. Results show that stochastic differential equatio…
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…
Influences des paramètres micromécaniques dans la simulation numérique discrète des matériaux granulaires : assemblage, déformation quasi-statique, écoulements
The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This…
Herein, we numerically study the rheology of a two-dimensional frictional granular system confined by constant pressure under oscillatory shear. Several scaling laws for the storage and loss moduli against the scaled strain amplitude have been found. The scaling laws in plastic regime for large strain amplitude can be understood by the angular distributions of the contact force. The scaling exponents are estimated by considering the physical mechanism.
We present a thorough study of the plastic response of a granular material progressively loaded. We study experimentally the evolution of the plastic field from a homogeneous one to an heterogeneous one and its fluctuations in term of incremental strain. We show that the plastic field can be decomposed in two components evolving on two decoupled strain increment scales. We argue that the slowly varying part of the field can be identified to the so-called fluidity field introduced recently to interpret the rheological behaviour of amorphous materials. This fluidity field progressively concentra…
The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using \emph{in situ} imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediatel…
We propose and numerically implement a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process. When dense, the material is treated as a pressure sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic flow rule given by the $μ(I)$ inertial rheology of granular materials. When the free volume exceeds a critical level, the material is deemed to separate and is treated as disconnected, stress-free media. A Material Point Method (MPM) procedure is written for the simulation of this model and many dem…
Magic Sand, a hydrophobic toy granular material, is widely used in popular science instructions because of its non-intuitive mechanical properties. A detailed study of the failure of an underwater column of magic sand shows that these properties can be traced to a single phenomenon: the system self-generates a cohesive skin that encapsulates the material inside. The skin, consists of pinned air-water-grain interfaces, shows multi-scale mechanical properties: they range from contact-line dynamics in the intra-grain roughness scale, plastic flow at the grain scale, all the way to the sample-scal…
We study the mobility of objects embedded in an immersed granular packing and subjected to cyclic loadings. In this aim, we conducted experiments using glass beads immersed in water and a horizontal plate subjected to a cyclic uplift force. Tests performed at different cyclic force frequencies and amplitudes evidence the development of three mobility regimes whereby the plate stays virtually immobile, moves up steadily or slowly creeps upwards. Results show that steady plate uplift can occur at lower force magnitudes when the frequency is increased. We propose an interpretation of this frequen…
We investigate the drag forces acting on large objects moving through a granular packing immersed in water. In this aim, we conducted uplift experiments involving pulling out horizontal plates at a prescribed velocity vertically. During these tests, we observed that the drag force reaches to peak at a low displacement and then decays. Results show that the peak drag force strongly increases with the velocity and depends on the plate size and grain diameter. We identify empirical scaling laws for these properties and introduce a Darcy-flow mechanism that can explain them. Furthermore, we conduc…
Macroscopic strain experiments revealed that Si crystals traversed by parallel, channel-like nanopores functionalized with the muscle polymer polypyrrole exhibit large and reversible electrochemo-mechanical actuation in aqueous electrolytes. On the microscopical level this system still bears open questions, as to how the electrochemical expansion and contraction of PPy acts on to np-Si pore walls and how the collective motorics of the pore array emerges from the single-nanopore behavior. An analysis of in operando X-ray diffraction experiments with micromechanical finite element simulations, b…
Logarithmic rate dependence in deforming granular materials
颗粒材料内部应力的速率无关性是许多缓慢稠密颗粒流模型的基本原则。相比之下，对数速率依赖性的应力被发现在固体对固体摩擦，在地质环境中，和其他地方。在这项工作中，我们表明，对数率依赖性发生在粒状材料的塑性（不可逆）变形，发生在剪切过程中，但不为弹性（可逆）变形，如那些发生在中度重复压缩。增加剪切速率Ω导致应力和应力波动的增加，这至少在定性上类似于由于密度增加而发生的情况。Ω的增加也导致应力积累和松弛事件的分布发生质的变化。如果剪切在t=0时停止，则发生应力松弛，σ（t）/ σ（t=0）\simeq A \log（t/t_0）。这种应力网络在几何上长时间的集体松弛提供了速率依赖性强化的机制。
We study the impact of a projectile onto a bed of 3 mm grains immersed in an index-matched fluid. Specifically, we vary the amount of prestrain on the sample, strengthening the force chains within the system. We find this affects only the prefactor of linear depth-dependent term in the stopping force. We therefore attribute this term to pressure within the material, and not the grain-intruder friction as is sometimes suggested. Using a laser sheet scanning technique to visualize internal grain motion, a high-speed camera, and particle tracking, we can measure the trajectory of each grain throu…
