Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the Boltzmann equation. A line of nontrivial fixed-point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively. Received 16 January 2002     

Erratum to: Directed force chain networks and stress response in static granular materials

The European Physical Journal E -     

不同条件下颗粒物质的粘弹性响应

研制了能承受100 MPa压强的测量装置,并用该装置对加压下制备的紧密沙堆进行粘弹性响应测量,得球形镍颗粒沙堆在周期性竖直振荡下储能模量G′与压强p 的关系. 实验结果表明,反映沙堆整体弹性特征的储能模G′与压强p 的关系为G′~p0.45;不同形状颗粒体系的粘弹性响应行为不同.     

Compactivity and transmission of stress in granular materials

We outline a statistical-mechanical theory of granular materials. Stress propagation and force fluctuations in static granular media are still poorly understood. We develop the statistical-mechanical theory that delivers the fundamental equations of stress equilibrium. The formalism is based on the assumptions that grains are rigid, cohesionless, and that friction is perfect. Since grains are assumed perfectly rigid, no strain or displacement field can enter the equations for static equilibrium of the stress field. The complete system of equations for the stress tensor is derived from the equations of intergranular force and torque balance, given the geometric specification of the material. These new constitutive equations are indeed fundamental and are based on relations between various components of the stress tensor within the material, and depend on the topology of the granular packing. The problem of incorporating into the formalism the "no tensile forces" constraint is considered. The compactivity concept is reviewed. We discuss the relation between the concept of compactivity and the problem of stress transmission. (c) 1999 American Institute of Physics.     

Janssen's law and stress fluctuations in confined dry granular materials

In order to clarify the mechanisms which determine the Janssen's law for the pressure distribution at the bottom of a silo we reconsider the so-called q-model describing an assembly of granular particles on a lattice, confined between vertical walls. We find that the expected macroscopic behavior with the correct scaling is obtained whenever a mechanism able to transfer the weight from the interior of the silo to the walls in an efficient way is present, i.e., in mean field regime. Deviations from the Janssen law's found in lattice models are due to the absence of this efficient mechanism. We investigate the scaling properties of a stick-slip model recently introduced, and find that relative fluctuations do not disappear for large systems and are of the order of average values. Finally we observe that an exponential local weight distribution at the bottom of the silo is independent of the model considered.     

The memory of granular materials

Granular materials exhibit a complex variety of fluid and solid collective regimes which has led researchers to consider them as a new state of matter all on its own. In this paper we investigate the behaviour of granular materials by means of Hurst rescaled range analysis. We analyse records in time of the angle of the slope of granular materials partially filling a rotating drum and records of the local backscattered light from fluidized beds. We show that the Hurst analysis is able to identify phase transitions as well as to characterize spatio-temporal structures. The influence of interparticle attractive interactions on the memory of granular materials is also investigated.     

Simulation of triaxial response of granular materials by modified DEM

A modified discrete element method(DEM)with rolling effect taken into consideration is developed to examine macroscopic behavior of granular materials in this study.Dimensional analysis is firstly performed to establish the relationship between macroscopic mechanical behavior,mesoscale contact parameters at particle level and external loading rate.It is found that only four dimensionless parameters may govern the macroscopic mechanical behavior in bulk.The numerical triaxial apparatus was used to study their influence on the mechanical behavior of granular materials.The parametric study indicates that Poisson’s ratio only varies with stiffness ratio,while Young’s modulus is proportional to contact modulus and grows with stiffness ratio,both of which agree with the micromechanical model.The peak friction angle is dependent on both inter-particle friction angle and rolling resistance.The dilatancy angle relies on inter-particle friction angle if rolling stiffness coefficient is sufficiently large.Finally,we have recommended a calibration procedure for cohesionless soil,which was at once applied to the simulation of Chende sand using a series of triaxial compression tests.The responses of DEM model are shown in quantitative agreement with experiments.In addition,stress-strain response of triaxial extension was also obtained by numerical triaxial extension tests.     

Wet granular materials

Most studies on granular physics have focused on dry granular media, with no liquids between the grains. However, in geology and many real world applications (e.g. food processing, pharmaceuticals, ceramics, civil engineering, construction, and many industrial applications), liquid is present between the grains. This produces inter-grain cohesion and drastically modifies the mechanical properties of the granular media (e.g. the surface angle can be larger than 90 degrees). Here we present a review of the mechanical properties of wet granular media, with particular emphasis on the effect of cohesion. We also list several open problems that might motivate future studies in this exciting but mostly unexplored field.

Wet granular materials

All authors

Namiko Mitarai &; Franco Nori

https://doi.org/10.1080/00018730600626065

Published online:

01 February 2007

Table     

垂直载荷下颗粒物质的声波探测和非线性响应

对于玻璃珠组成的颗粒介质样品,本文测量了横波和纵波声速,同时分析了剪切模量(G)与体积模量(B)的比值(G/B)随压强的变化规律.结果表明,在低压强下,颗粒体系的纵波声速(C_L)明显大于横波声速(c_T),且体系的CL,CT及G/B均随压强p变化呈幂律标度,即CL∝p~(0.3817),CT∝p~(0.2809)G/B∝p~(-0.4539),幂指数与文献[1]中预言的-1/2非常接近,暗示在我们实验压强范围内的颗粒样品处于L玻璃状态.此外,本文还利用快速傅里叶变换法测量了玻璃珠样品中的声学衰减特性及二阶谐波随压强的变化,发现:纵波声衰减系数(α)、接收端二倍频振幅(μ_(2ω))与基频振幅(μ_(1ω))平方的比值(μ_(2ω)/μ_(1ω)~2)均随压强的增大而幂率减小,分别为α∝p~-(-0.1879),和μ_(2ω)/μ_(1ω)~2∝p~(-0.866).     

Hall effect in granular materials

We show that in granular materials the Hall coefficient cannot, in general, be used to estimate directly the density of carriers, since it will depend on the ratio of the mobility within the grains to the conductivity mobility. The Hall voltage is predominantly determined within the individual grains, where the mobility may be quite large. On the other hand, the conductivity mobility may be considerably smaller due to a strong potential barrier between grains. The Hall coefficient depends on the ratio of these mobilities as well as on the carrier density.     

Memory effects in granular materials

We present a combined experimental and theoretical study of memory effects in vibration-induced compaction of granular materials. In particular, the response of the system to an abrupt change in shaking intensity is measured. At short times after the perturbation a granular analog of aging in glasses is observed. Using a simple two-state model, we are able to explain this short-time response. We also discuss the possibility for the system to obey an approximate pseudo-fluctuation-dissipation theorem relationship and relate our work to earlier experimental and theoretical studies of the problem.     

Ratcheting of granular materials

We investigate the quasistatic mechanical response of soils under cyclic loading using a discrete model of randomly generated convex polygons. This response exhibits a sequence of regimes, each one characterized by a linear accumulation of plastic deformation with the number of cycles. At the grain level, a quasiperiodic ratchetlike behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows exploration of the role of friction in the permanent deformation of unbound granular materials subjected to cyclic loading.     

Numerical study of the stress response of two-dimensional dense granular packings

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.     

Modeling force transmission in granular materials

The probability density function of contact forces in granular materials has been extensively studied and modeled as an outstanding signature of granular microstructure. Arguing that particle environments play a fundamental role in force transmission, we analyze the effects of steric constraints with respect to force balance condition and show that each force may be considered as resulting from a balance between lower and larger forces in proportions that mainly depend on steric effects. This idea leads to a general model that predicts an analytical expression of force density with a single free parameter. This expression fits well our simulation data and generically predicts the exponential fall-off of strong forces, a small peak below the mean force and the non-zero probability of vanishingly small forces.     

Avalanche dynamics in wet granular materials

We have studied the dynamics of avalanching wet granular media in a rotating drum apparatus. Quantitative measurements of the flow velocity and the granular flux during avalanches allow us to characterize novel avalanche types unique to wet media. We also explore the details of viscoplastic flow (observed at the highest liquid contents) in which there are lasting contacts during flow, leading to coherence across the entire sample. This coherence leads to a velocity-independent flow depth at high rotation rates and novel robust pattern formation in the granular surface.