Rigid Particles Research Articles

Discrete element modelling of the effect of aspect ratio on compaction and shear behaviour of aggregates

Coarse aggregates are essential for constructing railways and highways, as they affect structural performance through their compacted state and shear strength. Particle geometry influences these properties, but little research has quantitatively investigated how shape indexes impact mechanical indicators. This study addresses this gap by exploring the effect of particle aspect ratio on coarse aggregate compaction and shear behavior using the discrete element method (DEM). The study's key contribution is the development of novel equations that describe the correlation between packing porosity, inter-particle contact state, and aspect ratio control thresholds in a practical format. To do so, first, a point cloud database is compiled from laser scans of 700 natural aggregate particles. Each particle is classified using three aspect-ratio parameters: elongation, flatness, and flatness-elongation index (FEI). They are then digitized as rigid block particle models and compared against actual point clouds. Next, nine aggregates of representative shapes are assessed for their macro and mesoscopic mechanical responses using DEM-based vibro-compaction and direct shear tests. The compaction simulations indicate an exponential relationship between porosity and inter-particle coefficient of friction and show that aggregates with FEI ≈ 0.5 are a good choice. The direct shear simulations consider the same initial porosity, and show that the relationship between peak shear strength and vertical stress follows a power function. Finally, the analysis of contact forces and fabric tensors implies that FEI ≈ 0.5 may also facilitate particle fragmentation control.

Discrete-element method simulations of the seismic response of tunnels in deep granular deposit

The seismic response of tunnels constructed in a deposit of granular soil of depth greater than 20 m is examined in this paper. Three-dimensional discrete-element method (DEM) simulations were used to model the soil assembly and the tunnel lining. Soil particles were simulated as rigid spherical particles that are allowed to overlap at the contact points. The tunnel lining was modeled as a flexible system using a collection of particles that were glued together using cementitious bonds to mimic the physical properties of an actual tunnel. Free-field boundaries were utilized at the model’s lateral sides to prevent the propagating wave’s reflections back to the domain and enforce the free-field motion. The DEM computational framework was validated using published centrifuge test results. DEM simulation results reveal good agreement with the experimental centrifuge test results when subjected to the same input motion. Further simulations were carried out to investigate the seismic response of the system under different input motion characteristics. The dynamic earth pressure was monitored at certain points on the tunnel lining. It was found that the dynamic earth pressure and tunnel lining forces increased during seismic excitation and the final residual values were, in most cases, considerably larger than the initial static values. The results also showed that the maximum amplification factor, ground settlement and tunnel lining internal forces occurred close to the resonant frequency of the system.

Assessing Differential Particle Deformability under Microfluidic Flow Conditions.

Assessing the mechanical behavior of nano- and micron-scale particles with complex shapes is fundamental in drug delivery. Although different techniques are available to quantify the bulk stiffness in static conditions, there is still uncertainty in assessing particle deformability in dynamic conditions. Here, a microfluidic chip is designed, engineered, and validated as a platform to assess the mechanical behavior of fluid-borne particles. Specifically, potassium hydroxide (KOH) wet etching was used to realize a channel incorporating a series of micropillars (filtering modules) with different geometries and openings, acting as microfilters in the direction of the flow. These filtering modules were designed with progressively decreasing openings, ranging in size from about 5 down to 1 μm. Discoidal polymeric nanoconstructs (DPNs), with a diameter of 5.5 μm and a height of 400 nm, were realized with different poly(lactic-co-glycolic acid) (PLGA) and poly(ethylene glycol) (PEG) ratios (PLGA/PEG), namely, 5:1 and 1:0, resulting in soft and rigid particles, respectively. Given the peculiar geometry of DPNs, the channel height was kept to 5 μm to limit particle tumbling or flipping along the flow. After thorough physicochemical and morphological characterization, DPNs were tested within the microfluidic chip to investigate their behavior under flow. As expected, most rigid DPNs were trapped in the first series of pillars, whereas soft DPNs were observed to cross multiple filtering modules and reach the micropillars with the smallest opening (1 μm). This experimental evidence was also supported by computational tools, where DPNs were modeled as a network of springs and beads immersed in a Newtonian fluid using the smoothed particle hydrodynamics (SPH) method. This preliminary study presents a combined experimental-computational framework to quantify, compare, and analyze the characteristics of particles having complex geometrical and mechanical attributes under flow conditions.

Modeling and Experiments of Droplet Evaporation with Micro or Nano Particles in Coffee Ring or Coffee Splat.

Experimental and numerical experiments were carried out to study the coffee rings or coffee splats formed by droplet evaporation with micro or nano polystyrene sphere particles (Dp = 10 μm or 100 nm). Particle image velocimetry (PIV) and a high-resolution camera were used in this experiment, along with a temperature-controlled heater and a data-acquisition computer. The results showed that a nano particle could form a homogeneous coffee splat, instead of the common coffee ring formed when using micro particles. In order to account for this phenomenon, this paper developed a complex multiphase model, one which included the smooth particle hydrodynamics (SPH) fluid model coupled with the van der Waals equation of state for droplet evaporation, the rigid particle model of finite-size micro particles, and the point-particle model of the nanometer particles. The numerical simulation was operated on a GPU-based algorithm and tested by four validation cases. A GPU could calculate 533 times the speed of a single-core CPU for about 300,000 particles. The results showed that, for rigid solid particles, the forms emerged spontaneously on the wall, and their structure was mainly affected by the boundary wettability, and less affected by the fluid flow and thermal condition. When the wall temperature was low, it was easier for the particles to be deposited on the contact line. At high wall temperature, the coffee ring effect would be weakened, and the particles were more likely to be deposited in the droplet center. The hydrophilic surface produced a larger coffee ring compared to the hydrophobic surface. The experimental and numerical results proved that particle size could play a significant role during the particle deposition, which may be a possible route for producing uniform-distributed and nano-structure coatings.

Development of a toughened and antibacterial Poly(lactide acid) (PLA) with preserved strength by elemental sulfur-based bio-renewable dynamically crosslinked elastomers

The toughening of PLA is usually realized by blending with elastomers or plasticizers, but often conflicted with lowered mechanical strength and complicated preparation steps. In the current study, inverse vulcanization was used to synthesize a series of dynamically cross-linked polysulfide (SOA) elastomers based on refining by-product elemental sulfur, soybean oil (SO) and allyl glyceryl ether (AGE), which provides dynamically reversible S-S bonds, flexible triglyceride segments and reactive epoxy functions.Melt blended with PLA, the SOAs exhibit great toughening effects and produce droplet-matrix typed blends with good interfacial compatibilization verified by rheology. SOA composition was decisive in dictating toughening efficiency. A high AGE content induces self-polymerization of epoxy groups, resulting in dominance of permanent crosslinking in SOA, giving rise to rigid SOA particles with bad processability and dispersity in PLA, hence poor toughener cavitations under external forces with unsatisfying toughening effect. A high sulfur and low AGE content results in dominance of dynamic crosslinking, providing soft SOA particles in favor of processing and dispersion in PLA matrix with small domains and thin ligament thickness, thus favoring internal cavitation of SOA particles to achieve good toughness. However, the presence of unreacted sulfur with a too high sulfur content can mitigate the toughening effect. In particular, a highly toughened blend with optimized SOA composition (PLA-S50O25A25) was obtained with excellent toughness (elongation at break 235.7% and tensile toughness 76.5 MJ/m3) balanced by only slightly impaired strength (tensile strength 50–60 MPa and modulus ∼ 900 Mpa). Moreover, the PLA-SOA exhibits excellent broad-spectrum anti-bacterial effects. This study reported the unprecedented use of fully sustainable dynamically-crosslinked elastomers as tougheners of PLA, paving new ways for PLA modification with balanced stiffness-toughness and antibacterial activity.

Flow field disturbance due to point viscosity variations in a heterogeneous fluid

A fluid can be heterogeneous in either its density or viscosity - its two basic material properties. In this Letter, we ask how an ambient flow field is disturbed due to a point viscosity variation in the fluid. If we are able to answer this question, we can create an arbitrary spatial distribution of viscosity discretely by placing viscosity sources and sinks of appropriate strength, allowing us to model complex fluids. As an example, we show how the hydrodynamics of a rigid particle is altered due to the presence of point viscosity variations.

A strategy for improving negative-Poisson's-ratio constraint effect and shape accuracy of metamaterials by regulating mechanical properties of elastomer with facile filler incorporation

Negative Poisson's ratio (NPR) metamaterials are widely used for their light weight and good shear resistance. However, the essential concave hollow structures in NPR materials may easily distort irregularly when the constraint effect of their solid materials is weak, especially for elastomer-based materials. Here, we introduced nano-scale carbon black (CB) particles into the NPR material based on thermoplastic polyurethane (TPU) elastomers to control the static and dynamic mechanical deformation behavior of the material, improving their constraint effect on the NPR structure. The results show that the modulus of the NPR structure is improved by 269% by adjusting the unit and rigid particle load. The Poisson's ratio of the NPR structure reaches as great as −1.3 via controlling the thickness/width ratio (TWR) of the unit. Meanwhile, finite element analysis verifies that when TWR is less than 0.5, increasing the modulus and yield strength of the composites can enhance the constraint on the NPR unit. Theoretical calculation shows that CB introduced into TPU can improve the shape accuracy of NPR structure. Therefore, the work could offer a new mechanical enhancing strategy for NPR materials, and its application potential is verified as a form of exoskeletons.

ϕ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations

We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called ϕ-FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H1 norm for the velocity and L2 for pressure; numerically also in the L2 norm for the velocity).

Inertial migration of rigid red blood cell particles in Poiseuille flow

Inertial migration of single and multiple red blood cell (RBC) particles in a tube Poiseuille flow is studied using the lattice Boltzmann method coupled with the Galilean invariant momentum exchange method. Different blockage ratios, Reynolds numbers, and solid volume fractions are considered. In the single particle case, the RBC particle migrating in tumbling and rolling modes is called the tumbling particle and rolling particle, respectively. Simulation results show that the tumbling particle has a higher equilibrium position and longer rotation period than the rolling particle. For both the tumbling and rolling particles, when the blockage ratio increases, the equilibrium position moves closer to the tube centerline, and the rotation period becomes longer. The higher Reynolds number strongly affects the angular velocity of the RBC particle, leading the RBC particle to rotate faster; however, the equilibrium position is insensitive to the Reynolds number based on the limited observation. In the multiparticle case, the second and third inner particle annuluses unexpectedly form inside the Segré–Silberberg annulus as the solid volume fraction increases. Furthermore, smaller particles form the perfect Segré–Silberberg annulus at a lower solid volume fraction than larger particles. The third inner annulus of smaller particles is located further from the tube centerline than that of larger particles. This work is beneficial for understanding the motion of RBC particles in Poiseuille flow. It can positively contribute to the design of microfluidic devices for focusing, separating, and transporting red blood cells.

DEFORMATION PROPERTIES OF HIGHLY FILLED METAL-POLYMER COMPOSITIONS

The deformation behavior of model highly filled metal polymer aluminum powder compositions in polyethylene glycol under simultaneous action of compression and shear studied. The compression module increases with the increase of the compression, wherein the shear module significantly reduces. The discovered effect is related to the redistribution of the elastic layer between the rigid particles of the filler in the normal direction and in the shear area. The model of behavior of highly filled polymer compositions in these conditions proposed.

Dynamics of flexible fibers in confined shear flows at finite Reynolds numbers

We carry out a numerical study on the dynamics of a single non-Brownian flexible fiber in two-dimensional confined simple shear (Couette) flows at finite Reynolds numbers. We employ the bead-spring model of flexible fibers to extend the fluid particle dynamics (FPD) method that was originally developed for rigid particles in viscous fluids. We implement the extended FPD method using a multiple-relaxation-time scheme of the lattice Boltzmann method. The numerical scheme is validated first by a series of benchmark simulations that involve fluid–solid coupling. The method is then used to study the dynamics of flexible fibers in Couette flows. We only consider the highly symmetric cases where the fibers are placed on the symmetry center of Couette flows, and we focus on the effects of the fiber stiffness, the confinement strength, and the finite Reynolds number (from 1 to 10). A diagram of the fiber shape is obtained. For fibers under weak confinement and a small Reynolds number, three distinct tumbling orbits have been identified: (1) Jeffery orbits of rigid fibers—the fibers behave like rigid rods and tumble periodically without any visible deformation; (2) S-turn orbits of slightly flexible fibers—the fiber is bent to an S-shape and is straightened again when it orients to an angle of around 45° relative to the positive x-direction; and (3) S-coiled orbits of fairly flexible fibers—the fiber is folded to an S-shape and tumbles periodically and steadily without being straightened anymore during its rotation. Moreover, the fiber tumbling is found to be hindered by increasing either the Reynolds number or the confinement strength, or both.

Rigid rod particle like viscoelastic responses of poly(vinylidene fluoride) in N-methylpyrrolidone solution

A systematic study was performed on the dynamic viscoelastic properties of N-methylpyrrolidone (NMP) solutions of poly(vinylidene fluoride) (PVDF) samples with a wide range of weight average molar masses (Mw) from 140 to 3300 kg mol−1 over a temperature range of −24 to 35 °C in the dilute to semidilute concentration (c) regime in this study. In previous studies under extremely dilute conditions, it was confirmed that PVDF molecules behave as isolated highly elongated rigid rods, and the average particle length (⟨L⟩) and diameter (⟨d⟩) for different PVDF samples were precisely determined. The fundamental viscoelastic parameters used to analyze the dynamics of PVDF molecules dissolved in NMP were precisely determined, including the zero-shear shear viscosity (η0), the steady state compliance (Je), the average relaxation time (τw), and the activation energy (E*v) of τw in this study. E*v increased stepwise above c values corresponding to the reciprocal of the intrinsic viscosity ([η]−1) for different solutions, independent of Mw, showing that contact or the formation of entanglements between PVDF molecules causes the increase in E*v. Je−1 was found to be proportional to the number density of PVDF molecules (ν = cNAMw−1, where NA denotes the Avogadro constant) over the entire investigated v range, irrespective of Mw and the presence of entanglements between PVDF molecules. The reduced specific viscosities, ηspNA⟨L⟩3(Mw[η])−1, were reasonably described as a universal function in the parameter ν⟨L⟩3 over the entire investigated range, and ηspNA⟨L⟩3(Mw[η])−1 ∝ (ν⟨L⟩3)3 was found over the region 102 < ν⟨L⟩3 < 103, irrespective of Mw.

Continuum Percolation in Stochastic Homogenization and the Effective Viscosity Problem

This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard approaches in the literature have addressed this issue by making moment assumptions on interparticle distances. Such assumptions, however, prevent clustering of particles, which is not compatible with physically-relevant particle distributions. In this contribution, we take a different perspective and consider moment bounds on the size of clusters of close particles. On the one hand, assuming such bounds, we construct correctors and prove homogenization. On the other hand, based on subcritical percolation techniques, these bounds are shown to hold for various mixing particle distributions with nontrivial clustering. As a by-product of the analysis, we also obtain similar homogenization results for compressible and incompressible linear elasticity with unbounded random stiffness.

Simulation Study of Breakage in Coral Sand Particles under Dynamic Confined Compression

This paper reports a simulation-based dynamic confined compression analysis of coral sand under an impact load using the discrete element method (DEM). The evolution of particle breakage on the mesoscale was studied by investigating force chain distributions, crack development, and breakage modes. Crushable sand particles were simulated by replacing rigid particles with flexible basic unit aggregates. The Weibull parameters were incorporated within the mesoscopic parameters of particles, and random numbers were introduced. The obtained results for particle strengths were consistent with the experimental data. The numerical results demonstrated that the force chain was significantly strengthened along the loading axis during loading and weakened during unloading. The cracks were primarily generated along the strong force chain, and particle breakage caused the strong force chain to move towards relatively more complete fragments nearby. The crack was primarily oriented along the loading axis, and its anisotropy was observed to decrease with an increase in the load. Before yielding, particle breakage in the specimen was dominated by attrition at the edges and corners. After yielding, the crack extended into the particle perpendicular to the intergranular contact surface and was deflected by the simultaneous influence of pores. The fracture and shattering of particles occurred successively, and the consequent fall-off and slip filling of the fragments promoted the deformation development.

Numerical study of the formation and stability of a pair of particles of different sizes in inertial microfluidics

The formation of pairs and trains of particles in inertial microfluidics is an important consideration for device design and applications, such as particle focusing and separation. We study the formation and stability of linear and staggered pairs of nearly rigid spherical particles of different sizes in a pressure-driven flow through a straight duct with a rectangular cross section under mild inertia. An in-house lattice-Boltzmann-immersed-boundary-finite-element code is used for three-dimensional simulations. We find that the stability and properties of pairs of heterogeneous particles strongly depend on particle sizes and their size ratio, while the formation of the pairs is also determined by the initial lateral position and the axial order of the particles. Our findings imply that perturbations of particle trajectories caused by other particles, as they are expected to happen even in dilute suspensions, can be important for the formation of stable pairs in inertial microfluidics.

Direct numerical simulations of isolated rigid particles; Validation of smooth profile method

Direct numerical simulations of isolated rigid particles; Validation of smooth profile method

Microstructure and Nanoindentation Behavior of FeCoNiAlTi High-Entropy Alloy-Reinforced 316L Stainless Steel Composite Fabricated by Selective Laser Melting.

Selective laser melting (SLM) is one of the metal additive manufactured technologies with the highest forming precision, which prepares metal components through melting powders layer by layer with a high-energy laser beam. The 316L stainless steel is widely used due to its excellent formability and corrosion resistance. However, its low hardness limits its further application. Therefore, researchers are committed to improving the hardness of stainless steel by adding reinforcement to stainless steel matrix to fabricate composites. Traditional reinforcement comprises rigid ceramic particles, such as carbides and oxides, while the research on high entropy alloys as reinforcement is limited. In this study, characterisation by appropriate methods, inductively coupled plasma, microscopy and nanointendation assay, showed that we successfully prepared the FeCoNiAlTi high entropy alloy (HEA)-reinforced 316L stainless steel composites using SLM. When the reinforcement ratio is 2 wt.%, the composite samples show higher density. The SLM-fabricated 316L stainless steel displays columnar grains and it varies to equiaxed grains in composites reinforced with 2 wt.% FeCoNiAlTi HEA. The grain size decreases drastically, and the percentage of the low angle grain boundary in the composite is much higher than in the 316L stainless steel matrix. The nanohardness of the composite reinforced with 2 wt.% FeCoNiAlTi HEA is twice as high as the 316L stainless steel matrix. This work demonstrates the feasibility of using a high-entropy alloy as potential reinforcement in stainless steel systems.

Generalised Kelvin contact models for DEM modelling of asphalt mixtures

ABSTRACT Rigid particle models based on the discrete element method (DEM) have been adopted to model creep, fracture, and the viscoelastic behaviour of asphalt mixtures considering an irregular micro-structure and particle contacts. Within a DEM framework, the Burgers contact model, which is known to have a narrow frequency and temperature range, is usually adopted to model viscoelastic properties. In this study, a new explicit three-dimensional generalised Kelvin (GK) contact model formulation for the DEM model is proposed for asphalt materials. The model is implemented following two different methodologies (GK 1 and GK 2 ). The models are validated in uniaxial tension-compression sinusoidal tests for predicting the dynamic modulus ( | E ∗ | ) and phase angle (ϕ) of these composites at a frequency range of 1–10 Hz at 20 ∘ C. Four mixtures are investigated based on the modelling of their mastic. The influence of the GK contact parameters on the dynamic response of mastics is assessed. Results show that κ m has an important influence on both rheological properties and that η m can be used for small adjustments focussing on the predicted phase angle. Moreover, it is shown that a viscoelastic contact model should be adopted to simulate aggregate-to-mastic contacts in mixtures. As expected, the response obtained for both GK models is the same but the simulations with the GK 1 are 14% faster. In addition, the response predicted with the proposed GK contact model is compared with the response predicted with a Burgers contact model. The DEM predictions obtained for the GK model are more accurate. For mastics, the average errors for | E ∗ | and ϕ when adopting the GK model (Burgers) are 2.40% (3.46%) and 3.64% (4.17%), respectively. For mixtures, the average errors for | E ∗ | for the GK model (Burgers) are 7.00% (7.92%). The proposed contact model greatly enhances the DEM ability to simulate the viscoelasticity of asphalt materials.

Effect of Few-Layer Graphene on the Properties of Mixed Polyolefin Waste Stream

This work demonstrates how the addition of few-layer graphene (FLG) influences the processability and mechanical properties of the mixed polyolefin waste stream (R-(PE/PP)). Three different types of compounds were investigated: (1) R-(PE/PP) with FLG; (2) blends of R-(PE/PP) with prime polyethylene (PE) or polypropylene (PP) or PP copolymer; and (3) R-(PE/PP) with both the prime polymer and FLG. The processability was assessed by measuring the torque during melt extrusion, the melt flow index (MFI), and viscosity of the compounds. Investigations of the processability and mechanical properties of the composites indicate that the presence of FLG can reinforce the composites without hindering the processability, an unusual but desired feature of rigid fillers. A maximum increase in tensile strength by 9%, flexural strength by 23%, but a reduction in impact strength were observed for the compounds containing R-(PE/PP), 4 wt.% FLG, and 9 wt.% prime PP. The addition of FLG concentrations higher than 4 wt.% in R-(PE/PP), however, resulted in higher tensile and flexural properties while preserving the impact strength. Remarkably, the addition of 10 wt.% FLG increased the impact strength of the composite by 9%. This increase in impact strength is attributed to the dominant resistance of the rigid FLG particles to crack propagation.

Synthesis, Physicochemical Characterization and Applications of Advanced Nanomaterials

This Special Issue highlights the last decade's progress regarding new nanostructured materials. In this regard, the development of nanoscale syntheses and innovative characterization tools that resulted in the tailored design of nanostructured materials with versatile abilities in many applications were investigated. Various types of engineered nanostructures, usually metal nanoparticles or nanoporous metal oxides, have been synthesized for various applications. This Special Issue covers the state-of-the-art of advanced nanoparticles in many disciplines (chemistry, pharmacy, nanomedicine, agriculture, catalysis, and environmental science). The crystallite sizes depended on the annealing temperature and type of doping ion. A combination of rigid and soft particles could simultaneously enhance both the tensile properties and the fracture toughness, which could not be achieved by the single-phase particles independently. The surface charge and in vitro corrosion resistance are key parameters characterizing biomaterials in the interaction of the implant with the biological environment. Solar energy in the presence of a photocatalyst can be effectively converted into electricity/fuel, break down chemical and microbial pollutants, and help water purification. The saturation magnetization, remanent magnetizations, coercivity, and anisotropy were found to depend on the doping ion, annealing temperature, and particle size. The efficiency of the photocatalysis reaction depends on several factors, including light absorption capacity/light intensity, the type of photocatalyst used, the concentration of a photocatalyst and contaminant particles, the pH of the reaction medium, etc. The variety of color pigments and coloring properties of the targeted application in the ceramic industry was also of interest.