A contact model for the yielding of caked granular materials

We present a visco-elastic coupling model between caked spheres, suitable for Distinct Element Method simulations, which incorporates the different loading mechanisms (tension, shear, bending, torsion) in a combined manner and allows for a derivation of elastic and failure properties on a common basis. In pull, shear, and torsion failure tests with agglomerates of up to 10.000 particles, we compare the failure criterion to different approximative variants of it, with respect to accuracy and computational cost. The failure of the agglomerates, which behave according to elastic parameters derived from the contact elasticity, gives also insight into the relative relevance of the different load modes.     

The role of contact friction in the dynamic breakage behavior of granular materials

Based on the discrete element method, a multi-scale model is employed to investigate the role of contact friction in the dynamic compression responses of brittle granular materials. Four numerical granular samples with different particle friction coefficients ranging from 0.0 to 2.0 are tested and the particle breakage extent is quantified with the Einav breakage index. It is observed that the relationship of the breakage extent with the axial stress is apparently non-monotonic concerning the particle friction coefficient. At the same stress level, the breakage extent exhibits a minimum when the particle friction coefficient is around 0.1 but increases significantly with the particle friction coefficient to both sides. The micro physical origin of this non-monotonic behavior is a distinct transition in dominant particle-breakage modes from tension to shear. Moreover, energy analyses also show non-monotonic evolution of the frictional and damping dissipation with the particle friction coefficient. The joint effect of these two dissipation terms contributes to the non-monotonic behavior of particle breakage. In addition, the accuracy and competence of two frequently-used micro quantities, fraction of sliding contacts and average coordination number, are discussed.

     

A discrete model of a two-particle contact applied to cohesive granular materials

In this paper, we consider the complex problem of how to simulate particle contacts, taking into account the cohesion effect. In accordance with the molecular dynamics models, we propose a novel expression for the repulsive force which controls dynamically the transfer and dissipation of energy in granular media. This expression is formulated under fractional calculus, where a fractional derivative accumulates the whole history of the virtual overlap over time in weighted form. We then discuss and illustrate the basic properties of the repulsive force in a normal direction to the contacting surfaces. This approach allows us to perform simulations of arbitrary multiparticle contacts as well as granular cohesion dynamics.     

Stresses in granular materials

When circularly polarised light is passed through a granular material under boundary stresses patterns—‘light stripes’—are seen in the resulting images which have been traditionally associated with the directions of major principal stresses in the equivalent continuum. In this paper the passage of polarised light through a single spherical particle under stress is studied experimentally and analytically. The effect of placing the particle within a layer of particles, a layer of thickness 2–3 particles, and within a mass of particles is investigated experimentally. The appearance of light stripes is a visual reinforcement of effects seen at the particle level provided the level of stresses in individual particles is low. The implications for quantitative photoelastic interpretation of granular media are discussed.     

Mixtures of granular materials

Balance laws are given for a mixture of granular materials of a type described by Goodman and Cowin. Constitutive equations are given for the case of two dry granular constituents, and consequences of the entropy principle are found.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.     

Strong force networks in granular mixtures

Using the results of 3D discrete element method simulations we study the force transmission through binary mixtures of sand and silt sized spheres under one-dimensional compression. Three types of contact are categorized depending on the size of the two spheres in contact. The contributions of each contact type to the deviator stress are dependent on the proportion of silt sized spheres. We demonstrate that the magnitude of the deviator stress is solely due to the normal and tangential forces at contacts transmitting normal forces greater than a characteristic normal force, which is generally slightly greater than the average normal force. The maximum packing efficiency was obtained with the mixture of 30 % silt sized spheres and this mixture corresponds to a transition point when there are enough silt sized particles to start to separate the sand sized particles from each other and establish contacts between silt sized spheres that contribute to the deviator stress.     

Modeling soft granular materials

Soft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction.     

Asymptotic behaviour of granular materials

The concept of the asymptotic behaviour of particulate materials is described, including its enhancement by considering asymptotic states in extension. A 3D discrete element model with elastic spherical particles and the granulometry of a real sand is set up. The numerical sample is stretched from different initial states, and the influence of the strain rate direction on the final state is studied within the stress ratio, void ratio and mean stress space. Asymptotic behaviour is clearly observed, although the grains remain intact (no grain crushing is considered). The extension asymptotic states were observed, and the notion of a normal extension line is introduced. The extension asymptotic states coincide with the peak states observed in the shear tests with constant stress path direction in dense samples.     

Gravitational flow of granular materials

The free flow of granular materials through an orifice in a horizontal bottom has been investigated. An equation is proposed for calculating the mass flow rate.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 15, No. 5, pp. 870–874, November, 1968.     

Stochastic process of fracture in granular materials

By regarding the coefficient of particle friction of granular materials as a random variable distributed on the particle surface, the mechanism of particle sliding is interpreted as a stochastic process. Axial, shearing and volumetric strains are defined with regard to the deformation of a microscopic regular assembly of uniform spheres. For illustration, these strains are calculated for a uniform distribution of the coefficient of particle friction and applied to some triaxial test results reported elsewhere.     

Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model

An adhesive elasto-plastic contact model for the discrete element method with three dimensional non-spherical particles is proposed and investigated to achieve quantitative prediction of cohesive powder flowability. Simulations have been performed for uniaxial consolidation followed by unconfined compression to failure using this model. The model has been shown to be capable of predicting the experimental flow function (unconfined compressive strength vs. the prior consolidation stress) for a limestone powder which has been selected as a reference solid in the Europe wide PARDEM research network. Contact plasticity in the model is shown to affect the flowability significantly and is thus essential for producing satisfactory computations of the behaviour of a cohesive granular material. The model predicts a linear relationship between a normalized unconfined compressive strength and the product of coordination number and solid fraction. This linear relationship is in line with the Rumpf model for the tensile strength of particulate agglomerate. Even when the contact adhesion is forced to remain constant, the increasing unconfined strength arising from stress consolidation is still predicted, which has its origin in the contact plasticity leading to microstructural evolution of the coordination number. The filled porosity is predicted to increase as the contact adhesion increases. Under confined compression, the porosity reduces more gradually for the load-dependent adhesion compared to constant adhesion. It was found that the contribution of adhesive force to the limiting friction has a significant effect on the bulk unconfined strength. The results provide new insights and propose a micromechanical based measure for characterising the strength and flowability of cohesive granular materials.     

Properties of force networks in jammed granular media

Discrete element method simulations are conducted to investigate the effects of applied uniaxial compressive load, and bidisperse particle size distributions on force networks within jammed granular media. The differences between the strong and weak networks are examined through investigating the spatial correlation and distribution of contact angles, and emergence of chainlike structures. The simulation results show that the chainlike structures are more prevalent in the strong network due to the larger cumulative probabilities of contact angles, but not all the contacts belonging to the strong or weak networks are able to constitute the chainlike structures. Although the contacts of coarse-fine particles are dominant for the bidisperse systems, the contacts of coarse–coarse particles dominate the strong network, as well as the linear chainlike structures. Upon increasing the pressure from very low to high, the probability of contact orientations with respect to the compression direction in the strong network increases for contact orientation less than \(60^{\circ }\) and decreases for contact orientation greater than \(60^{\circ }\), while the opposite trends are observed in the weak network. The tails of normalized normal contact forces distributions are quantified by \(\hbox {P}(\hbox {f}) = \hbox {exp}(-\hbox {cf}^{\mathrm{n}})\), and it is found that the value of n depends on the applied pressure and particle size distribution. Statistical analysis shows that the degree of homogeneity of contact force increases with increasing pressure, which is also validated by participation number.     

Dilatant plastic deformation of granular materials

A geometrical interpretation is given to the modified associated flow rule derived in the previous paper[l]. According to it, the dilatancy must be regarded as an internal constraint of deformation. The modified associated flow rule then gives equations of plastic deformation which exhibits the specified dilatancy. Hardening and elastic strains can also be incorporated. It is shown that the deformation is non-coaxial in general.     

Effective thermal conductivity of granular materials

Some fundamental works whose authors propose formulas to calculate the thermal conductivities of granular materials are presented.     

On fluidization of polydisperse granular materials

A method has been developed for calculating the fractional composition of boiling bed particles liquefied at a given speed of filtration with account for the composition of the supplied granular materials. The relation between the maximum size of particles and their mean diameter and the degree of polydispersity has been investigated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 353–357, March–April, 2008.