Unique Viscoelasticity and Hierarchical Relaxation Dynamics of Molecular Granular Materials

Resulting from the dense packing of subnanometer molecular clusters, molecular granular materials (MGMs) are shown to maintain high elasticity far above their apparent glass transition temperature (Tg*). However, our microscopic understanding of their structure-property relationship is still poor. Herein, 1 nm polyhedral oligomeric silsesquioxanes (POSSs) are appended to a backbone chain in a brush configuration with different flexible linker chains. Assemblies of these brush polymers exhibit hierarchical relaxation dynamics with the glass transition arising from the cooperative dynamics of packed POSSs. The interaction among the assemblies can be strengthened by increasing the rigidity of linkers with the MGM relaxation modes changing from colloid- to polymer chain-like behavior, rendering their tunable viscoelasticity. This finally contributes to the decoupling of mechanical and thermal properties by showing elasticity dominant mechanical properties at a temperature 150 K above the Tg*.

3D DEM Analysis of Particle Breakage Effect on Direct Shear Tests of Coarse Sand

This paper explores the effect of particle breakage on the mechanical behavior of coarse sand through 3D Discrete Element Method (DEM) simulations of direct shear tests (DST). The objective is to gain insights into the macro- and micro-mechanical behaviors of crushable coarse sand, with a particular focus on the stress-strain relationship, volumetric deformation, and evolution of grain crushing. The simulations involve a comparison between non-crushable and crushable particle models, where the crushable particles are implemented in the shear zone of the DST subjected to different high normal stresses. The findings indicate that the crushable particles experience partial crushing at peak shear stress, with further particle crushing leading to the production of finer particles at the shearing plane during shearing at the critical state. The migration of these finer particles under pressure and gravity generates their accumulation predominantly in the lower section of the simulation box. Importantly, the presence of crushing in the DST induces a decrease in the shear stress and an increase in the volumetric strain leading to contractive behavior instead of dilation, which gradually stabilizes the volumetric deformation at higher normal stresses.

Identify the Micro-Parameters for Optimized Discrete Element Models of Granular Materials in Two Dimensions Using Hexagonal Close-Packed Structures

The widely used simple cubic-centered (SCC) model structure has limitations in handling diagonal loading and accurately representing Poisson's ratio. Therefore, the objective of this study is to develop a set of modeling procedures for granular material discrete element models (DEM) with high efficiency, low cost, reliable accuracy, and wide application. The new modeling procedures use coarse aggregate templates from an aggregate database to improve simulation accuracy and use geometry information from the random generation method to create virtual specimens. The hexagonal close-packed (HCP) structure, which has advantages in simulating shear failure and Poisson's ratio, was employed instead of the SCC structure. The corresponding mechanical calculation for contact micro-parameters was then derived and verified through simple stiffness/bond tests and complete indirect tensile (IDT) tests of a set of asphalt mixture specimens. The results showed that (1) a new set of modeling procedures using the hexagonal close-packed (HCP) structure was proposed and was proved to be effective, (2) micro-parameters of the DEM models were transit form material macro-parameters based on a set of equations that were derived based on basic configuration and mechanism of discrete element theories, and (3) that the results from IDT tests prove that the new approach to determining model micro-parameters based on mechanical calculation is reliable. This new approach may enable a wider and deeper application of the HCP structure DEM models in the research of granular material.

On the Vibration-Damping Properties of the Prestressed Polyurethane Granular Material

Granular materials promise opportunities for the development of high-performance, lightweight vibration-damping elements that provide a high level of safety and comfort. Presented here is an investigation of the vibration-damping properties of prestressed granular material. The material studied is thermoplastic polyurethane (TPU) in Shore 90A and 75A hardness grades. A method for preparing and testing the vibration-damping properties of tubular specimens filled with TPU granules was developed. A new combined energy parameter was introduced to evaluate the damping performance and weight-to-stiffness ratio. Experimental results show that the material in granular form provides up to 400% better vibration-damping performance as compared to the bulk material. Such improvement is possible by combining both the effect of the pressure-frequency superposition principle at the molecular scale and the effect of the physical interactions between the granules (force-chain network) at the macro scale. The two effects complement each other, with the first effect predominating at high prestress and the second at low prestress. Conditions can be further improved by varying the material of the granules and applying a lubricant that facilitates the granules to reorganize and reconfigure the force-chain network (flowability).

Estimation of the Acoustic Properties of the Random Packing Structures of Granular Materials: Estimation of the Sound Absorption Coefficient Based on Micro-CT Scan Data

In this study, the sound absorption properties of randomly packed granular materials were estimated. Generally, it is difficult to construct a general mathematical model for the arrangement of randomly packed granular materials. Therefore, in this study, an attempt was made to estimate the sound absorption coefficient using a theoretical analysis by introducing data from computed tomography (CT) scans, as the tomographic images of CT scans correspond to the slicing and elemental division of packing structures. In the theoretical analysis, the propagation constants and characteristic impedances in the voids were obtained by approximating each tomographic image as a void between two parallel planes. The derived propagation constants and characteristic impedances were then treated as a one-dimensional transfer matrix in the propagation of sound waves, and the transfer matrix method was used to calculate the normal incident sound absorption coefficient. The theoretical value of the sound absorption coefficient was derived using the effective density to which the measured tortuosity was applied. As a result, for the theoretical values considering the tortuosity, in many cases, the theoretical values were close to the measured values. For the theoretical values, when both the surface area and tortuosity were considered, the peak sound absorption frequency moved to a lower frequency and was in general agreement with the measured values.

Dynamically structured bubbling in vibrated gas-fluidized granular materials

The dynamics of granular materials are critical to many natural and industrial processes; granular motion is often strikingly similar to flow in conventional liquids. Food, pharmaceutical, and clean energy processes utilize bubbling fluidized beds, systems in which gas is flowed upward through granular particles, suspending the particles in a liquid-like state through which gas voids or bubbles rise. Here, we demonstrate that vibrating these systems at a resonant frequency can transform the normally chaotic motion of these bubbles into a dynamically structured configuration, creating reproducible, controlled motion of particles and gas. The resonant frequency is independent of particle properties and system size, and a simple harmonic oscillator model captures this frequency. Discrete particle simulations show that bubble structuring forms because of rapid, local transitions between solid-like and fluid-like behavior in the grains induced by vibration. Existing continuum models for gas-solid flows struggle to capture these fluid-solid transitions and thus cannot predict the bubble structuring. We propose a constitutive relationship for solids stress that predicts fluid-solid transitions and hence captures the experimental structured bubbling patterns. Similar structuring has been observed by oscillating gas flow in bubbling fluidized beds. We show that vibrating bubbling fluidized beds can produce a more ordered structure, particularly as system size is increased. The scalable structure and continuum model proposed here provide the potential to address major issues with scale-up and optimal operation, which currently limit the use of bubbling fluidized beds in existing and emerging technologies.

Viscous flow and collapse of macroscopic cavities in a granular material in terms of a Darcylet

Viscous flow through a granular material that has a macroscopic cavity is obtained on the basis of the Stokes and the generalized Darcy's equation. A new singularity termed 'Darcylet', a fundamental flow in the granular material that acts like a point force with negative direction, is proposed, which is applied to elucidate the interaction of two cavities. Depending on the configuration of the latter, the volume flux into the cavity increases, which enhances the local stresses on the boundary, causes the collapse of cavities and triggers landslides. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Gravitational instabilities in binary granular materials

The motion and mixing of granular media are observed in several contexts in nature, often displaying striking similarities to liquids. Granular dynamics occur in geological phenomena and also enable technologies ranging from pharmaceuticals production to carbon capture. Here, we report the discovery of a family of gravitational instabilities in granular particle mixtures subject to vertical vibration and upward gas flow, including a Rayleigh-Taylor (RT)-like instability in which lighter grains rise through heavier grains in the form of "fingers" and "granular bubbles." We demonstrate that this RT-like instability arises due to a competition between upward drag force increased locally by gas channeling and downward contact forces, and thus the physical mechanism is entirely different from that found in liquids. This gas channeling mechanism also generates other gravitational instabilities: the rise of a granular bubble which leaves a trail of particles behind it and the cascading branching of a descending granular droplet. These instabilities suggest opportunities for patterning within granular mixtures.

Dynamic Pore-Scale Model of Drainage in Granular Porous Media: The Pore-Unit Assembly Method

Dynamics of drainage is analyzed for packings of spheres, using numerical experiments. For this purpose, a dynamic pore-scale model was developed to simulate water flow during drainage. The pore space inside a packing of spheres was extracted using regular triangulation, resulting in an assembly of grain-based tetrahedra. Then, pore units were constructed by identifying and merging tetrahedra that belong to the same pore, resulting in an assembly of pore units. Each pore unit was approximated by a volume-equivalent regular shape (e.g., cube and octahedron), for which a local capillary pressure-saturation relationship was obtained. To simulate unsaturated flow, a pore-scale version of IMPES (implicit pressure solver and explicit saturation update) was employed in order to calculate pressure and saturation distributions as a function of time for the assembly of pore units. To test the dynamic model, it was used on a packing of spheres to reproduce the corresponding measured quasi-static capillary pressure-saturation curve for a sand packing. Calculations were done for a packing of spheres with the same grain size distribution and porosity as the sand. We obtained good agreement, which confirmed the ability of the dynamic code to accurately describe drainage under low flow rates. Simulations of dynamic drainage revealed that drainage occurred in the form of finger-like infiltration of air into the pore space, caused by heterogeneities in the pore structure. During the finger-like infiltration, the pressure difference between air and water was found to be significantly higher than the capillary pressure. Furthermore, we tested the effects of the averaging, boundary conditions, domain size, and viscosity on the dynamic flow behavior. Finally, the dynamic coefficient was determined and compared to experimental data.

Gravisensors in plant cells behave like an active granular liquid

Plants are able to sense and respond to minute tilt from the vertical direction of the gravity, which is key to maintain their upright posture during development. However, gravisensing in plants relies on a peculiar sensor made of microsize starch-filled grains (statoliths) that sediment and form tiny granular piles at the bottom of the cell. How such a sensor can detect inclination is unclear, as granular materials like sand are known to display flow threshold and finite avalanche angle due to friction and interparticle jamming. Here, we address this issue by combining direct visualization of statolith avalanches in plant cells and experiments in biomimetic cells made of microfluidic cavities filled with a suspension of heavy Brownian particles. We show that, despite their granular nature, statoliths move and respond to the weakest angle, as a liquid clinometer would do. Comparison between the biological and biomimetic systems reveals that this liquid-like behavior comes from the cell activity, which agitates statoliths with an apparent temperature one order of magnitude larger than actual temperature. Our results shed light on the key role of active fluctuations of statoliths for explaining the remarkable sensitivity of plants to inclination. Our study also provides support to a recent scenario of gravity perception in plants, by bridging the active granular rheology of statoliths at the microscopic level to the macroscopic gravitropic response of the plant.

Effect of Anisotropy on the Resilient Behaviour of a Granular Material in Low Traffic Pavement

Granular materials are often used in pavement structures. The influence of anisotropy on the mechanical behaviour of granular materials is very important. The coupled effects of water content and fine content usually lead to more complex anisotropic behaviour. With a repeated load triaxial test (RLTT), it is possible to measure the anisotropic deformation behaviour of granular materials. This article initially presents an experimental study of the resilient repeated load response of a compacted clayey natural sand with three fine contents and different water contents. Based on anisotropic behaviour, the non-linear resilient model (Boyce model) is improved by the radial anisotropy coefficient γ₃ instead of the axial anisotropy coefficient γ₁. The results from both approaches (γ₁ and γ₃) are compared with the measured volumetric and deviatoric responses. These results confirm the capacity of the improved model to capture the general trend of the experiments. Finally, finite element calculations are performed with CAST3M in order to validate the improvement of the modified Boyce model (from γ₁ to γ₃). The modelling results indicate that the modified Boyce model with γ₃ is more widely available in different water contents and different fine contents for this granular material. Besides, based on the results, the coupled effects of water content and fine content on the deflection of the structures can also be observed.

Force Transmission Modes of Non-Cohesive and Cohesive Materials at the Critical State

This paper investigates the force transmission modes, mainly described by probability density distributions, in non-cohesive dry and cohesive wet granular materials by discrete element modeling. The critical state force transmission patterns are focused on with the contact model effect being analyzed. By shearing relatively dense and loose dry specimens to the critical state in the conventional triaxial loading path, it is observed that there is a unique critical state force transmission mode. There is a universe critical state force distribution pattern for both the normal contact forces and tangential contact forces. Furthermore, it is found that using either the linear Hooke or the non-linear Hertz model does not affect the universe force transmission mode, and it is only related to the grain size distribution. Wet granular materials are also simulated by incorporating a water bridge model. Dense and loose wet granular materials are tested, and the critical state behavior for the wet material is also observed. The critical state strength and void ratio of wet granular materials are higher than those of a non-cohesive material. The critical state inter-particle distribution is altered from that of a non-cohesive material with higher probability in relatively weak forces. Grains in non-cohesive materials are under compressive stresses, and their principal directions are mainly in the axial loading direction. However, for cohesive wet granular materials, some particles are in tension, and the tensile stresses are in the horizontal direction on which the confinement is applied. The additional confinement by the tensile stress explains the macro strength and dilatancy increase in wet samples.

The Quantified Characterization Method of the Micro-Macro Contacts of Three-Dimensional Granular Materials on the Basis of Graph Theory

We have attempted a multiscale and quantified characterization method of the contact in three-dimensional granular material made of spherical particles, particularly in cemented granular material. Particle contact is defined as a type of surface contact with voids in its surroundings, rather than a point contact. Macro contact is a particle contact set satisfying the restrictive condition of a two-dimensional manifold with a boundary. On the basis of graph theory, two dual geometrical systems are abstracted from the granular pack. The face and the face set, which satisfies the two-dimensional manifold with a boundary in the solid cell system, are extracted to characterize the particle contact and the macro contact, respectively. This characterization method is utilized to improve the post-processing in DEM (Discrete Element Method) from a micro perspective to describe the macro effect of the cemented granular material made of spherical particles. Since the crack has the same shape as its corresponding contact, this method is adopted to characterize the crack and realize its visualization. The integral failure route of the sample can be determined by a graph theory algorithm. The contact force is assigned to the weight value of the face characterizing the particle contact. Since the force vectors can be added, the macro contact force can be solved by adding the weight of its corresponding faces.