Vibrational dynamics of confined granular materials

High-pressure compacted recycled polymeric composite waste materials for marine applications

Abstract

Options for recycling fiber composite polymer (FCP) materials are scarce, as these materials cannot be normally recycled and are toxic when improperly disposed. Additionally, reducing water usage is an increasing concern, as the concrete industry currently uses 10% of the world’s industrial water. Therefore, building upon our previous work, this research explores the use of polymer hybrid carbon and glass composite waste products as reinforcements in high-pressure compacted cement. Our material used nearly 70% less water during manufacturing and exhibited improved durability and salt corrosion resistance. Compression strength tests were performed on high-pressure compacted materials containing 6.0 wt% recycled admixtures before and after saltwater aging, and the results showed that the material retained 90% of its original compression strength after aging, as it contained fewer pores and cavities. Our experimental work was supplemented by molecular dynamics. Simulations, which indicated that the synergetic effects of compaction and FCP admixture addition slowed the diffusion of corrosive salt ions by an average of 84%. Thus, our high-pressure compacted cement material may be suitable for extended use in marine environments, while also reducing the amount of commercial fiber composite polymer waste material that is sent to the landfill.

Article Highlights

Simulating direct shear tests with the Bullet physics library: A validation study

This study focuses on the possible uses of physics engines, and more specifically the Bullet physics library, to simulate granular systems. Physics engines are employed extensively in the video gaming, animation and movie industries to create physically plausible scenes. They are designed to deliver a fast, stable, and optimal simulation of certain systems such as rigid bodies, soft bodies and fluids. This study focuses exclusively on simulating granular media in the context of rigid body dynamics with the Bullet physics library. The first step was to validate the results of the simulations of direct shear testing on uniform-sized metal beads on the basis of laboratory experiments. The difference in the average angle of mobilized frictions was found to be only 1.0°. In addition, a very close match was found between dilatancy in the laboratory samples and in the simulations. A comprehensive study was then conducted to determine the failure and post-failure mechanism. We conclude with the presentation of a simulation of a direct shear test on real soil which demonstrated that Bullet has all the capabilities needed to be used as software for simulating granular systems.

Rheology of granular materials composed of crushable particles

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Bonded-cell model for particle fracture

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.

Effect of size polydispersity versus particle shape in dense granular media

We present a detailed analysis of the morphology of granular systems composed of frictionless pentagonal particles by varying systematically both the size span and particle shape irregularity, which represent two polydispersity parameters of the system. The microstructure is characterized in terms of various statistical descriptors such as global and local packing fractions, radial distribution functions, coordination number, and fraction of floating particles. We find that the packing fraction increases with the two parameters of polydispersity, but the effect of shape polydispersity for all the investigated structural properties is significant only at low size polydispersity where the positional and/or orientational ordering of the particles prevail. We focus in more detail on the class of side/side contacts, which is the interesting feature of our system as compared to a packing of disks. We show that the proportion of such contacts has weak dependence on the polydispersity parameters. The side- side contacts do not percolate but they define clusters of increasing size as a function of size polydispersity and decreasing size as a function of shape polydispersity. The clusters have anisotropic shapes but with a decreasing aspect ratio as polydispersity increases. This feature is argued to be a consequence of strong force chains (forces above the mean), which are mainly captured by side-side contacts. Finally, the force transmission is intrinsically multiscale, with a mean force increasing linearly with particle size.

Packings of irregular polyhedral particles: strength, structure, and effects of angularity

We present a systematic numerical investigation of the shear strength and structure of granular packings composed of irregular polyhedral particles. The angularity of the particles is varied by increasing the number of faces from 8 (octahedronlike shape) to 596. We find that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below 46 faces). At the same time, the packing fraction increases to a peak value but declines for more angular particles. We analyze the connectivity and anisotropy of the microstructure by considering both the contacts and branch vectors joining particle centers. The increase of the shear strength with angularity is shown to be due to a net increase of the fabric and force anisotropies but at higher particle angularity a rapid falloff of the fabric anisotropy is compensated by an increase of force anisotropy, leading thus to the saturation of shear strength.

Rheology of three-dimensional packings of aggregates: microstructure and effects of nonconvexity

We use three-dimensional contact dynamics simulations to analyze the rheological properties of granular materials composed of rigid aggregates. The aggregates are made from four overlapping spheres and described by a nonconvexity parameter depending on the relative positions of the spheres. The macroscopic and microstructural properties of several sheared packings are analyzed as a function of the degree of nonconvexity of the aggregates. We find that the internal angle of friction increases with the nonconvexity. In contrast, the packing fraction first increases to a maximum value but declines as the nonconvexity increases further. At a high level of nonconvexity, the packings are looser but show a higher shear strength. At the microscopic scale, the fabric and force anisotropy, as well as the friction mobilization, are enhanced by multiple contacts between aggregates and interlocking, thus revealings the mechanical and geometrical origins of shear strength.

Effect of confinement on dense packings of rigid frictionless spheres and polyhedra

We study numerically the influence of confinement on the solid fraction and on the structure of three-dimensional random close-packed granular materials subject to gravity. The effects of grain shape (spherical or polyhedral), material polydispersity, and confining wall friction on this dependence are investigated. In agreement with a simple geometrical model, the solid fraction is found to decrease linearly for increasing confinement no matter the grain shape. Furthermore, this decrease remains valid for bidisperse sphere packings, although the gradient seems to reduce significantly when the proportion of small particles reaches 40% by volume. The confinement effect on the coordination number is also captured by an extension of the aforementioned model.

Nonlinear effects of particle shape angularity in sheared granular media

We analyze the effects of particle shape angularity on the macroscopic shear behavior and texture of granular packings simulated by means of the contact dynamics method. The particles are regular polygons with an increasing number of sides ranging from 3 (triangles) to 60. The packings are analyzed in the steady shear state in terms of their shear strength, packing fraction, connectivity, and fabric and force anisotropies, as functions of the angularity. An interesting finding is that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below six sides). In contrast, the packing fraction declines towards a constant value, so that the packings of more angular particles are looser but have higher shear strength. We show that the increase of the shear strength at low angularity is due to an increase of both contact and force anisotropies and the saturation of the shear strength for higher angularities is a consequence of a rapid falloff of the contact and normal force anisotropies compensated for by an increase of the tangential force anisotropy. This transition reflects clearly the rather special geometrical properties of these highly angular shapes, implying that the stability of the packing relies strongly on the side-side contacts and the mobilization of friction forces.

Discrete simulation of dense flows of polyhedral grains down a rough inclined plane

The influence of grain angularity on the properties of dense flows down a rough inclined plane are investigated. Three-dimensional numerical simulations using the nonsmooth contact dynamics method are carried out with both spherical (rounded) and polyhedral (angular) grain assemblies. Both sphere and polyhedra assemblies abide by the flow start and stop laws, although much higher tilt angle values are required to trigger polyhedral grain flow. In the dense permanent flow regime, both systems show similarities in the bulk of the material (away from the top free surface and the substrate), such as uniform values of the solid fraction, inertial number and coordination number, or linear dependency of the solid fraction and effective friction coefficient with the inertial number. However, discrepancies are also observed between spherical and polyhedral particle flows. A dead (or nearly arrested) zone appears in polyhedral grain flows close to the rough bottom surface, reflected by locally concave velocity profiles, locally larger coordination number and solid fraction values, smaller inertial number values. This dead zone disappears for smooth bottom surfaces. In addition, unlike sphere assemblies, polyhedral grain assemblies exhibit significant normal stress differences, which increase close to the substrate.

Force chains and contact network topology in sheared packings of elongated particles

By means of contact dynamic simulations, we investigate the contact network topology and force chains in two-dimensional packings of elongated particles subjected to biaxial shearing. The morphology of large packings of elongated particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and orientations of contacts between particles. The effect of elongation on shear behavior and dilatancy was investigated in detail in a previous paper [Azéma and Radjai, Phys. Rev. E 81, 051304 (2010)]. Here, we show how particle elongation affects force distributions and force-fabric anisotropy via various local structures allowed by steric exclusions and the requirement of force balance. We find that the force distributions become increasingly broader as particles become more elongated. Interestingly, the weak force network transforms from a passive stabilizing agent with respect to strong force chains to an active force-transmitting network for the whole system. The strongest force chains are carried by side-side contacts oriented along the principal stress direction.

Stress-strain behavior and geometrical properties of packings of elongated particles

We present a numerical analysis of the effect of particle elongation on the quasistatic behavior of sheared granular media by means of the contact dynamics method. The particle shapes are rounded-cap rectangles characterized by their elongation. The macroscopic and microstructural properties of several packings subjected to biaxial compression are analyzed as a function of particle elongation. We find that the shear strength is an increasing linear function of elongation. Performing an additive decomposition of the stress tensor based on a harmonic approximation of the angular dependence of branch vectors, contact normals, and forces, we show that the increasing mobilization of friction force and the associated anisotropy are key effects of particle elongation. These effects are correlated with partial nematic ordering of the particles which tend to be oriented perpendicular to the major principal stress direction and form side-to-side contacts. However, the force transmission is found to be mainly guided by cap-to-side contacts, which represent the largest fraction of contacts for the most elongated particles. Another interesting finding is that, in contrast to shear strength, the solid fraction first increases with particle elongation but declines as the particles become more elongated. It is also remarkable that the coordination number does not follow this trend so that the packings of more elongated particles are looser but more strongly connected.

Short-time dynamics of a packing of polyhedral grains under horizontal vibrations

We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall subjected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dynamics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short-time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency.

Force transmission in a packing of pentagonal particles

We perform a detailed analysis of the contact force network in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The effect of particle shape is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics, except for the circular shape of the particles. A counterintuitive finding of this work is that, under steady shearing, the pentagon packing develops a lower structural anisotropy than the disk packing. We show that this weakness is compensated by a higher force anisotropy, leading to enhanced shear strength of the pentagon packing. We revisit "strong" and "weak" force networks in the pentagon packing, but our simulation data also provide evidence for a large class of "very weak" forces carried mainly by vertex-to-edge contacts. The strong force chains are mostly composed of edge-to-edge contacts with a marked zigzag aspect and a decreasing exponential probability distribution as in a disk packing.