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.     

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.     

DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material

The mechanical behavior of granular materials is largely affected by particle breakage. Physical and mechanical properties of granular materials, such as grain size distribution, deviatoric and volumetric behavior, compressibility and mobilized friction angle are affected by particle crushing. This paper focuses on the evolution of the above mentioned characteristics using the Discrete Element Method (DEM). Behaviors of stiff and soft materials are studied using well established crushing criteria. Results from simulations indicate that stiff materials, have a typical fractal distribution of particle size, which is dominant when confining pressure increases. The fractal characteristic parameter of grain size effect is discussed. Evolution of shear stresses and volumetric strains during shearing are also predicted and analyzed. Expanded perlite, selected as a soft material, is investigated in terms of shear and volumetric behavior. For perlite, triaxial compression tests and corresponding DEM simulations are also performed. Results show good agreement between experiments and simulations and support the fact that the DEM can be considered as a useful tool to predict the behavior of crushable granular materials.     

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.     

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.     

Stress partition analysis of granular materials

Writing the stress as a sum over contact forces allows one to partition stress increments according to their microscopic, grain-level causes. We present two ways of doing this: the first way differentiates between normal and tangential contact forces, while the second ascribes different parts of a change in stress to different physical processes such as contact network anisotropy, non-affine motions and sliding contacts. These two partitioning methods can be combined. We then use them to analyze simulations of failure in biaxial tests, leading to several results. We show that the granular material becomes effectively frictionless well before failure. In addition, by partitioning the second order work, one can attribute a part of the destabilization to each of the various physical processes mentioned above.     

Effective properties of cemented granular materials

An analytical model is developed to describe the effective elastic properties of a cemented granular material that is modeled as a random packing of identical spheres. The elastic moduli of grains may differ from those of cement. The effective bulk and shear moduli of the packing are calculated from geometrical parameters (the average number of contacts per sphere and porosity), and from the normal and tangential stiffnesses of a two-grain combination. The latter are found by solving the problems of normal and tangential deformation of two elastic spherical grains cemented at their contact. A thin cement layer is approximated by an elastic foundation, and the grain-cement interaction problems are reduced to linear integral equations. The solution reveals a peculiar distribution pattern of normal and shear stresses at the cemented grain contacts: the stresses are maximum at the center of the contact region when the cement is soft relative to the grain, and are maximum at the periphery of the contact region when the cement is stiff. Stress distribution shape gradually varies between these two extremes as the cement's stiffness increases. The solution shows that it is mainly the amount of cement that influences the effective elastic properties of cemented granular materials. The radius of the cement layer affects the stiffness of a granular assembly much more strongly than the stiffness of the cement does. This theoretical model is supported by experimental results.     

Reconfigurable nanoscale soft materials

We discuss recent research efforts towards understanding and implementing the physical rules needed to make materials—especially materials composed of nanoscale building blocks—that exhibit the defining characteristics of living systems: adaptive and evolving functional behavior. In particular, we highlight advancements in direct imaging and quantifying of kinetic pathways governing structural reconfiguration in model systems of colloidal nanoparticles as well as emerging opportunities brought by frontier efforts in synthesizing shape-shifting colloids and flexible electronics. Direct observation of kinetic “crossroads” in nanoparticle self-assembly and reconfiguration will offer insight into how these steps can be manipulated to design dynamic, potentially novel materials and devices. Moreover, these principles will not be limited to nanoparticles; when extended to building blocks like soft micelles and proteins, they have the potential to have a similar impact throughout the broader field of soft matter physics.     

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.