Elastic Particles Research Articles

Effective Elastic Properties of 3-Phase Particle Reinforced Composites with Randomly Dispersed Elastic Spherical Particles of Different Sizes

Higher-order multiscale structures are proposed to predict the effective elastic properties of 3-phase particle reinforced composites by considering the probabilistic spherical particles spatial distribution, the particle interactions, and utilizing homogenization with ensemble volume average approach. The matrix material, spherical particles with radius a₁, and spherical particles with radius a₂, are denoted as the 0^th phase, the 1^st phase, and the 2^nd phase, respectively. Particularly, the two inhomogeneity phases are different particle sizes and the same elastic material properties. Improved higher-order (in ratio of spherical particle sizes to the distance between the centers of spherical particles) bounds on effective elastic properties of 3-phase particle reinforced proposed Formulation II and Formulation I derive composites. As a special case, i.e., particle size of the 1^st phase is the same as that of the 2^nd phase, the proposed formulations reduce to 2-phase formulas. Our theoretical predictions demonstrate excellent agreement with selected experimental data. In addition, several numerical examples are presented to demonstrate the competence of the proposed frameworks.

Thermal conductivity of PbTe-CoSb3 bulk polycrystalline composite: role of microstructure and interface thermal resistance.

Systematic experimental and theoretical research on the role of microstructure and interface thermal resistance on the thermal conductivity of the PbTe-CoSb3 bulk polycrystalline composite is presented. In particular, the correlation between the particle size of the dispersed phase and interface thermal resistance (Rint) on the phonon thermal conductivity (κph) is discussed. With this aim, a series of PbTe-CoSb3 polycrystalline composite materials with different particle sizes of CoSb3 was prepared. The structural (XRD) and microstructural analysis (SEM/EDXS) confirmed the intended chemical and phase compositions. Acoustic impedance difference (ΔZ) was determined from measured sound velocities in PbTe and CoSb3 phases. It is shown that κph of the composite may be reduced when particle size of the dispersed phase (CoSb3) is smaller than the critical value of ∼230 nm. This relationship was concluded to be crucial for controlling the heat transport phenomena in composite thermoelectric materials. The selection of the components with different elastic properties (acoustic impedance) and particle size smaller than Kapitza radius leads to a new direction in the engineering of composite TE materials with designed thermal properties.

Filtration of Elastic Polymers and Spherical Gels through a Silica-Deposited Layer on a Porous Membrane

A 120-nm silica suspension was permeated through a porous polyethylene (PE) hollow-fiber membrane, as was a solution of deformable elastic particles of poly(N-isopropylacrylamide) (PNIPAM) gel and dextran. The amount adsorbed and flux of permeation were analyzed with ordinary differential equations to obtain adsorption coefficients, maximum amounts adsorbed, and pore-narrowing factors. The thickness of the “silica-deposited layer” on the membrane was 1 μm. In a batch adsorption mode, 5.0 mg of PNIPAM gel and 30 mg of dextran were adsorbed on the PE membrane, with no adsorption on the silica. The PE membrane pores were narrowed by a secondary layer of adsorbed PNIPAM gel. When filtered through the silica-deposited layer, PNIPAM gel occupies gaps, resulting in a reduced permeation flux. Dextran passed through the silica-deposited layer and was partially adsorbed on the PE membrane. The modified membrane can control adsorption, filtration, and flux permeation, which leads to dynamic membrane separations.

A simplified formula to estimate the size of the cyclic plastic zone in metals containing elastic particles

The applicability of Irwin’s estimate to metals containing particles becomes dubious when the plastic zone (PZ) size is comparable to the particle spacing. Therefore, a multiscale model is used to investigate the crack tip plasticity in a cyclically loaded elastic-perfectly plastic matrix containing a realistic distribution of spherical particles. Homogenization and dimensional analysis demonstrate that the PZ shape differs from what is expected based on von Mises plasticity. The scaling of the PZ size with the square of the stress intensity factor is confirmed, but the proportionality coefficient is strongly affected by the particle volume fraction. Consequently, a new compact formula for the PZ size is proposed, which holds for material properties ranging from metal matrix composites to cast irons and is robust to minor particle deviations from the spherical shape.

Failure processes of cemented granular materials.

The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here we use a discrete element model simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular medium with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure, and compaction banding or anticracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow, and foam.

Syneresis of Colloidal Gels: Endogenous Stress and Interfacial Mobility Drive Compaction.

Colloidal gels may experience syneresis, an increase in volume fraction through expulsion of the continuous phase. This poroelastic process occurs when adhesion to the container is weak compared to endogenous stresses which develop during gelation. In this work, we measure the magnitude of syneresis, ΔV/V_{0}, for gels composed of solid, rubber, and liquid particles. Surprisingly, despite a constant thermoresponsive interparticle potential, gels composed of liquid and elastic particles synerese to a far greater extent. We conclude that this magnitude difference arises from contrasting modes of stress relaxation within the colloidal gel during syneresis either by bending or stretching of interparticle bonds.

Reflection of a shock wave from a finely dispersed medium of low concentrations

A model of a shock tube is prepared to study the behaviour of a shock wave in a layer of light elastic granular particles. Computational experiments are made using the OpenFOAM package. The prepared model allows carrying out simulations for pressure between 105 and 104 Pa and concentration of particles of 20%. Results are obtained on pressures in different time moments, depending on different densities of granular particles. An increase of the density of the granular particles is shown to decrease the blurring of the boundary between the media. It is also noted that a decrease in the density leads to double pressure peaks.

Acoustic radiation force acting on a heavy particle in a standing wave can be dominated by the acoustic microstreaming

When an acoustic wave scatters on a particle the acoustic radiation force and the microstreaming appear as non-linear time-averaged effects. Although they appear simultaneously, the microstreaming, which is driven by viscous losses, is often neglected in the theoretical modeling of the acoustic radiation force. Here, we investigate the contribution of the acoustic microstreaming to the acoustic radiation force acting on a small elastic spherical particle placed into an ultrasonic standing wave [T. Baasch, A. Pavlic, and J. Dual, Phys. Rev. E 100(6), 061102 (2019)]. The compressible Navier-Stokes equations are solved up to second-order in terms of the small Mach number using a finite element method. Our study shows that above a certain viscosity, when the viscous boundary layer thickness to particle radius ratio is sufficiently large, the contribution of the microstreaming dominates the acoustic radiation force and defines the stable position of the particle, provided that the particle is sufficiently dense. In such cases (e.g., combination of a copper particle of 1 μm radius in a mineral oil), our theory predicts migration of the particle to the pressure antinode.

Rotating tensiometer for the measurement of the elastic modulus of deformable particles

In a spinning drop tensiometer, the interfacial tension between two immiscible liquids can be inferred from the equilibrium shape of a drop suspended in a rotating medium. Similarly, an analytical solution is derived for the deformation dynamics of an initially spherical elastic particle suspended in a denser viscous rotating liquid. This gives a proof of concept for a rotating tensiometer for the measurement of the mechanical properties of soft solid beads. Direct numerical simulations are used to validate the theory and identify its limits of applicability.

Acoustic Radiation Force on a Spherical Fluid or Solid Elastic Particle Placed Close to a Fluid or Solid Elastic Half-Space

The acoustic radiation force acting on a spherical particle placed close to the interface of two infinite half-spaces that is excited by a normally incident traveling wave is investigated using the finite element method (FEM). The medium surrounding the particle is water, whereas different material models are used for the particle itself and the second half-space. Recently, acoustic force spectroscopy has been developed, a technology that uses acoustic forces to measure the mechanical properties of small filaments. If acoustics are used to manipulate particles that are placed very close to an interface then the acoustic interactions between the particle and interface lead to an acoustic interaction force. This interaction force was neglected in previous studies and is included in the total acoustic radiation force obtained by our FEM model. Comparing our results to the primary radiation force that can be obtained using the Gor'kov potential, we found that, for cells (red blood cells or fat cells) immersed in water and placed close to a PMMA, glass, or silicon domain, the magnitude of the acoustic interaction force can exceed 10% of the magnitude of the primary radiation force. In other cases, the acoustic interaction force can be even larger in amplitude and of opposite sign than the primary force.

Recycling Tire-Derived Aggregate as elastic particles under railway sleepers: Impact on track lateral resistance and durability

The use of recycled Tire-Derived Aggregate (TDA) under railway sleepers has been demonstrated to be a sustainable and effective way to improve the durability and mechanical behaviour of ballasted train tracks. This solution enables the optimization of a track’s vertical performance, as different rubber quantities can be employed depending on track vertical requirements, while recycling a waste material abundantly available. However, before the widespread adoption of TDA, joined to previous studies focused on track vertical behaviour, it is still necessary to assess its influence on the lateral resistance of the track, given the importance of this parameter on the infrastructure’s quality and safety. Thus, the present paper focused on determining the effects on the lateral resistance of the section when employing varying quantities of rubber particles under the sleeper, along with its impact depending on the level of track degradation. For this study, laboratory tests were carried out to simulate realistic traffic conditions on full-scale sections. Results showed that TDA under sleepers could lead to higher lateral oscillations of the track due to the flexibility of the rubber particles, but resulting in similar, or even lower, permanent displacements to those in conventional ballasted tracks, as long as not excessive rubber volumes are applied. Particularly, for the study cases assessed in this article, it was seen that quantities up to around 1500–2000 cm3 (applied under half sleeper) could reduce permanent lateral movements due to dynamic efforts up to 45% in reference to traditional ballasted tracks, while increasing close to 130% the number of loads required to reach a lateral displacement of 10 mm (selected as example of failure criteria).

Stochastic Approach to the Solution of Boussinesq-Like Problems in Discrete Media

A vertical surface load acting on a half-space made of discrete and elastic particles is supported by a network of force chains that changes with the specific realization of the packing. These force chains can be transformed into equivalent stress fields, but the obtained values are usually different from those predicted by the unique solution of the corresponding boundary value problem. In this research the relationship between discrete and continuum approaches to Boussinesq-like problems is explored in the light of classical statistical mechanics. In the principal directions of the stress established by the continuum-based approach, the probability distribution functions of the extensive normal and shear stresses of particles are anticipated to be exponential and Laplace distributions, respectively. The extensive stress is the product of the volumetric average of the stress field within a region by the volume of that region. The parameters locating and scaling these probability distribution functions (PDFs) are such that the expected values of the extensive stresses match the solution to the corresponding boundary value problem: zero extensive shear stress and extensive normal stresses equal to the principal ones. The continuum-based approach is still needed to know the expected values, but this research article presents a powerful method for quantifying their expected variability. The theory has been validated through massive numerical simulation with the discrete element method. These results could be of interest in highly fragmented, faulted or heterogeneous media or on small length scales (with particular applications for laboratory testing).

Microgels at Interfaces Behave as 2D Elastic Particles Featuring Reentrant Dynamics

Soft colloids are increasingly used as model systems to address fundamental issues such as crystallisation and the glass and jamming transitions. Among the available classes of soft colloids, microgels are emerging as the gold standard. Since their great internal complexity makes their theoretical characterization very hard, microgels are commonly modelled, at least in the small-deformation regime, within the simple framework of linear elasticity theory. Here we show that there exist conditions where its range of validity can be greatly extended, providing strong numerical evidence that microgels adsorbed at an interface follow the two-dimensional Hertzian theory, and hence behave like 2D elastic particles, up to very large deformations, in stark contrast to what found in bulk conditions. We are also able to estimate the Young's modulus of the individual particles and, by comparing it with its counterpart in bulk conditions, we demonstrate a significant stiffening of the polymer network at the interface. Finally, by analyzing dynamical properties, we predict multiple reentrant phenomena: by a continuous increase of particle density, microgels first arrest and then re-fluidify due to the high penetrability of their extended coronas. We observe this anomalous behavior in a range of experimentally accessible conditions for small and loosely crosslinked microgels. The present work thus establishes microgels at interfaces as a new model system for fundamental investigations, paving the way for the experimental synthesis and research on unique high-density liquidlike states. In addition, these results can guide the development of novel assembly and patterning strategies on surfaces and the design of novel materials with desired interfacial behavior.

Electroelastic Response of Isotropic Dielectric Elastomer Composites with Deformation-Dependent Apparent-Permittivity Matrix

AbstractThis paper puts forth an approximate yet accurate free energy for the elastic dielectric response—under finite deformations and finite electric fields—of non-percolative dielectric elastomer composites made out of a non-Gaussian dielectric elastomer matrix with deformation-dependent apparent permittivity isotropically filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. While the proposed free energy applies in its most general form to arbitrary isotropic non-percolative microstructures, closed-form specializations are recorded for the practically relevant cases of rigid or liquid-like spherical particles. The proposed free energy is exact by construction in the asymptotic context of small deformations and moderate electric fields and is shown to remain accurate for arbitrary large deformations and electric fields via comparisons with full-field finite-element simulations. The proposed constitutive model is deployed to probe the electrostriction response of these dielectric elastomer composites and corresponding results reveal that their elastic dielectric response strongly depends on the deformation-dependent apparent permittivity of the matrix they comprise.

Using FEM to study the frictional instability induced by third-body particles confined in frictional interface

Purpose A finite element method (FEM) model of the frictional behavior of two rough surfaces with a group of third-body particles confined by the surface asperities is established. By monitoring the stress distribution, friction force and the displacement of the surfaces, how the frictional instability is induced by these particles is studied. This modeling job aims to explore the relation between the meso-scale behavior and the macro-scale frictional behavior of these particles. Design/methodology/approach By using FEM, a 2D model of two frictional rough surfaces with a group of elastic or elasto-plastic particles confined by surface asperities is established. The Mises stress, macro friction force and displacements of elements are monitored during compressing and shearing steps. Findings The macro friction coefficient is more stable under higher pressure and smaller under higher shearing speed. The dilatancy of the interface is caused by the elevation effect of the particles sheared on the peak of the lower surface, particles collision and third body supporting. The combined effect of particles motion and surface–surface contact will induce high-frequency displacements of surface units in restricted direction. Originality/value Previous studies about third-body tribology are mainly concentrated on the frictional behavior with large number of particles distributed homogeneously across the interface, but this paper focuses on the behavior of third-body particles confined by surface asperities. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2019-0544/

Development of Elastic Drag Coefficient Model and Explicit Terminal Settling Velocity Equation for Particles in Viscoelastic Fluids

Summary Viscoelastic fluids are frequently used as drilling or fracturing fluids to enhance cuttings or proppant transport efficiency. The solid transport performance of these fluids largely depends on the settling behaviors of suspended particles. Different from viscoinelastic fluids, the elastic and viscous characteristics of viscoelastic fluids both affect particle settling behaviors. In this study, to separately quantify the contribution degrees of the shear viscosity and fluid elasticity on the terminal settling velocity, we decompose the total drag force into a viscous drag force and an elastic drag force. Based on the experimental data from the available literature, it is concluded that the elastic drag force is a function of the fluid elasticity, particle diameter, particle terminal settling velocity, and density difference between the fluid and particle. The formula for the elastic drag force is determined on the basis of the force analysis, and a relationship between the elastic drag coefficient and particle Reynolds number (Re) is developed. An explicit equation that directly predicts the terminal settling velocity in viscoelastic fluids is determined by correlating the dimensionless particle diameter and Re. To validate the proposed model, a total of 108 settling experiments in viscoelastic fluids are conducted. The absolute percentage error (APE) between the predicted and measured terminal settling velocities is 15.26%, which indicates that the proposed explicit terminal settling velocity equation can provide satisfactory prediction accuracy of the terminal settling velocity for particles in viscoelastic fluids. Furthermore, an illustrative example is provided to show that the proposed model can be used to calculate the required fluid elasticity to obtain the desired terminal settling velocity when the fluid shear viscosity is fixed. The proposed models are valid with a consistency index range of approximately 0.16 to 1.2 Pa⋅sn, flow behavior index range of approximately 0.282 to 0.579, an Re range of approximately 0.005 to 30, and a fluid relaxation time range of approximately 0.183 to 110 seconds. This study can help operators choose proper drilling/fracturing fluids to enhance the cuttings/proppant transport and maximize drilling/fracturing performance.

Interaction between particles and bubbles driven by ultrasound: Acoustic radiation force on an elastic particle immersed in the ideal fluid near a bubble.

A theoretical model is proposed to investigate the acoustic radiation force on the elastic particle for coupled particle-bubble system. Based on the sound scattering theory, an analytical expression of the force function is obtained for the particle in plane wave sound field. Numerical simulations are presented for elastic particle of stainless steel, steel or brass. The results reveal that the presence of bubbles can affect the feature of radiation force curves of particles. The force curve fluctuates, and negative force emerges in the small kR1 region for certain distance between the bubble and particle. There are more sharp peaks and dips in the curves because of the resonance of the elasticity of the system and the resonant peaks of the acoustic radiation force transfer to low frequencies when the size of elastic particle is increased. The approximate positive flat region is shortened because of the presence of bubble, which may help to optimize the size ranges of particle for acoustic screening. This study provides for improvement of the acoustic manipulation theoretical model.

A Coarse Grained Model for Viscoelastic Solids in Discrete Multiphysics Simulations

Viscoelastic bonds intended for Discrete Multiphysics (DMP) models are developed to allow the study of viscoelastic particles with arbitrary shape and mechanical inhomogeneity that are relevant to the pharmaceutical sector and that have not been addressed by the Discrete Element Method (DEM). The model is applied to encapsulate particles with a soft outer shell due, for example, to the partial ingress of moisture. This was validated by the simulation of spherical homogeneous linear elastic and viscoelastic particles. The method is based on forming a particle from an assembly of beads connected by springs or springs and dashpots that allow the sub-surface stress fields to be computed, and hence an accurate description of the gross deformation. It is computationally more expensive than DEM, but could be used to define more effective interaction laws.

Modular “Solitons”: Mutual Absorption and Annihilation in Dissipative Media

Collisions of two pulsed signals in a medium with modular (M) nonlinearity and a special relaxation law are investigated. The processes are described by an integro-differential equation, the kernel of which is nonzero in a finite time interval. It is believed that within this interval, the “memory of the medium” is constant, but outside it, it vanishes. For this model, the analysis is reduced to solving a simple differential-difference equation, whereas the volume of computations is significantly reduced. The phenomena accompanying pulse collisions of are described: nonlinear mutual attenuation, annihilation, and signal broadening with time. The effect of the signal parameters and properties of the medium on these processes is explained. The collision of two modular solitons described by the Korteweg–de Vries M-equation is considered. It is shown that, by using this model, the interaction may differ from the usual behavior of solitons, revealing an analogy with elastic particle interaction.

Angle- and azimuth-domain common-image gathers by reverse time migration for 3D elastic isotropic media

A 2D algorithm for angle-domain common-image gather (CIG) calculation is extended and modified to produce 3D elastic angle and azimuth CIGs. The elastic seismic data are propagated with the elastic particle displacement wave equation, and then the PP-reflected and PS-converted waves are separated by divergence and curl calculations during application of the excitation-time imaging condition. The incident angles and azimuths are calculated using source propagation directions and the reflector normals. The source propagation direction vector is computed as the spatial gradient of the incident 3C P-wavefield. The vector normal to the reflector is calculated using the Hilbert transform. Ordering the migrated images with respect to incident angles for a fixed azimuth bin, or with respect to azimuths for a fixed incident angle bin, creates angle- or azimuth-domain CIGs, respectively. Sorting the azimuth gathers by the incident angle bins causes a shift to a greater depth for too-high migration velocity and to a smaller depth for too-low migration velocity. For the sorted incident angle gathers, the velocity-dependent depth moveout is within the angle gathers and across the azimuth gathers. This method is compared with three other 3D CIG algorithms with respect to the number of calculations and their disk storage and RAM requirements; it is three to six orders of magnitude faster and requires two to three orders of magnitude less disk space. The method is successfully tested with data for a modified part of the SEG/EAGE overthrust model.