Effective properties of cemented granular materials

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

Two-dimensional bioluminescence tomography: numerical simulations and phantom experiments

The reconstruction of internal light sources in bioluminescence tomography (BLT) is a challenging inverse problem because of the limited amount of information available compared with that for other kinds of tomography such as fluorescence tomography in which external illumination sources are used. We demonstrated previously, using phantom experiments, that a target containing luciferases could be detected tomographically when the target was located relatively close to the imaging boundary. Here we describe an improved BLT reconstruction method that can detect luciferase-containing targets located anywhere within an imaging domain. The method is tested with numerical simulations and further confirmed with several phantom experiments.     

Solitary wave trains in granular chains: experiments,theory and simulations

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains’ masses and the striker mass. Numerical calculations and experiments corroborate these findings.     

An investigation on loose cemented granular materials via DEM analyses

This paper presents the results of a numerical study carried out by 2D discrete element method analyses on the mechanical behavior and strain localization of loose cemented granular materials. Bonds between particles were modeled in order to replicate the mechanical behavior observed in a series of laboratory tests performed on pairs of glued aluminum rods which can fail either in tension or shear (Jiang et al. in Mech Mater 55:1–15, 2012). This bond model was implemented in a DEM code and a series of biaxial compression tests employing lateral flexible boundaries were performed. The influence of bond strength and confinement levels on the mechanical behavior and on the onset of shear bands and their propagation within the specimens were investigated. Comparisons were also drawn with other bond models from the literature. A new dimensionless parameter incorporating the effects of both bond strength and confining pressure, called BS, was defined. The simulations show that shear strength and also dilation increase with the level of bond strength. It was found out that for increasing bond strength, shear bands become thinner and oriented along directions with a higher angle over the horizontal. It also emerged that the onset of localization coincided with the occurrence of bond breakages concentrated in some zones of the specimens. The occurrence of strain localization was associated with a concentration of bonds failing in tension.     

Three-scale modeling and numerical simulations of fabric materials

Based on the underlying structure of fabric materials, a three-scale model is developed to describe the mechanical behavior of fabric materials. The current model assumes that fabric materials take on an overall behavior of anisotropic membranes, thus the membrane-scale is taken as the macroscopic scale of the model. Since fabric materials exist only as thin structures and there is no corresponding bulk material having a similar constitutive property, the direct approach of the mechanics of surfaces is employed. Following the membrane-scale, a yarn-scale is introduced, in which yarns and their weaving structure are accounted for explicitly. Yarns are modeled as an extensible elasticae. A unit cell consisting of two overlapping yarns is used to formulate the weaving patterns and the interaction between the yarns, which governs the nonlinear constitutive behavior of fabric materials. The third scale, named fibril-scale, accounts for the fibrils constituting a yarn and incorporates their mechanical properties. Via a coupling (handshake) process between these three scales a couple model is introduced. The overall behavior and performance of various fabric products becomes predictable by the knowledge of the material properties of a single fibril and the weaving structure of the fabrics. In addition, potential damage during deformation is also captured in the current model through breakage of fibrils in the fibril-scale.     

Shock dynamics in granular chains: numerical simulations and comparison with experimental tests

The aim of this paper is to simulate the nonlinear wave propagation in granular chains of beads using a recently introduced multiple impact model and to compare numerical results to experimental ones. Different kinds of granular chains are investigated: monodisperse chains, tapered chains and stepped chains. Particular attention is paid to the dispersion effect, and the wave propagation in tapered chains, the interaction of two solitary waves in monodisperse chains, and the formation of solitary wave trains in stepped chains. We show that the main features of the wave propagation observed experimentally in these granular chains are very well reproduced. This proves that the considered multiple impact model and numerical scheme are able to encapsulate the main physical effects that occur in such multibody systems.     

Mechanistic investigation of mixing and segregation of ordered mixtures: experiments and numerical simulations

Pulmonary delivery of cohesive and micronized drugs through dry powder inhalers (DPIs) is traditionally achieved through the formation of ordered mixtures. In order to improve the mechanistic understanding of formation of ordered mixtures, the system consisting of micronized lactose (AZFL, representative of an active pharmaceutical ingredient) and a coarse particle carrier (LH100) is investigated as a function of different process and material variables in a high shear mixer (HSM) and in a low shear double cone (DCN) blender, using both experimental and numerical methods. Process insight is developed using a Discrete Element Method (DEM) based numerical model which could predict the formation of ordered mixtures in the two blenders and was verified against experimental determinations. Spatial and temporal evolution of granular flow are visualized and quantified in silico to reveal distinguishing features of both blenders to aid in rational selection of blenders and process parameters.     

A wire-woven cellular metal: Part-II, Evaluation by experiments and numerical simulations

Wire-woven bulk Kagome (WBK) is a new truss-type cellular metal fabricated by systematic assembly of helical wires in six directions. In Part-I of this work, analytic solutions for equivalent material properties, such as yield stress and elastic modulus of WBK under compression and shear were derived. The load capacities of a WBK-cored sandwich panel under bending were predicted for various failure modes, and optimal designs of the WBK-cored sandwich panel were determined. In this work, the overall performance of a WBK-cored sandwich panel under shear and bending loads were evaluated in more detail by experiment and finite element (FE) simulation. Using comparisons with our experimental and numerical results, we show that the simple analytic solutions obtained in Part-I gave effective and accurate solutions. Hence, the model optimally designed on the basis of the analytic solutions gave the expected results. Furthermore, the WBK-cored sandwich panel showed excellent performance in terms of load capacity, energy absorption, and deformation stability after the maximum load point.     

Evolution of meso-structures and mechanical properties of granular materials under triaxial compression state from complex network perspective

The evolution of the network connection of granular materials is investigated by performing a series of numerical simulations in triaxial compression tests with different initial porosities by discrete element method (DEM). Results of evolution characteristics of complex network are reported for both dense and loose assembles. The simulation focuses on the influence of porosity on connectivity evolution, and reveals the correlation between the parameters in macro and mesoscale. Kinds of properties are studied, including degree and its distribution, clustering coefficient, network density and the average shortest path. The results demonstrate the phenomenon of dilataion due to shear deformation are able to be reflected by those mesocope parameters mentioned. Specifically, in the process of the dilatation, the rate of contact disintegration exceeds the rate of contact creation, which means the loss of connectivity, thus the values of some properties decrease, like degree, clustering coefficient and network density, but some increase like the average shortest path. Additionally, the bridging of macro and mesoscope are built regarding the parameters of the Cam-Clay model and complex network. From the results, the parameter M (determined by q?=?Mp′ at critical state) and the reference parameter \( {\text{T}} \) (\( T_{j}^{s} = L_{j}^{s} \left( {1 - \log_{{D_{j}^{s} }} t} \right) \), calculated according to the average degree \( D_{j}^{s} \) and shortest path \( L_{j}^{s} \) of the critical state) have a positive correlation. And a linear relationship between the slope of isotropic virgin-consolidation λ and the rate of decline of the average shortest path upon loading is represented as well. These achievements are the first step in an ongoing study of establishing the multi-scale constitutive from complex network perspective.     

Critical state behaviour of granular materials from isotropic and rebounded paths: DEM simulations

This paper presents the results of numerical simulations using the three-dimensional discrete element method (DEM) on the critical state behaviour of isotropically compressed and rebounded assemblies of granular materials. Drained and undrained (constant volume) numerical simulations were carried out. From these numerical simulations of drained and undrained tests, it has been shown that the steady state is same as the critical state. Critical state for both isotropically compressed and rebounded assemblies form unique curved line that can be approximated by a bilinear line as proposed by Been et al. [Géotechnique 41(3): 365–381, 1991]. Further more, evolution of the internal variables such as average coordination number and induced anisotropy coefficients during shear deformation has been studied.     

Stick-slip behaviour of model granular materials in drained triaxial compression

Drained triaxial axisymmetric compression tests are performed on water-saturated short cylindrical samples of nearly monodisperse glass beads, initially assembled in a loose state by a moist tamping technique. Both deviator stress $q$ and volumetric strain $\epsilon _v$ , measured as functions of axial strain $\epsilon _a$ , for different strain rates, are affected by stick-slip events of very large amplitude, while the classical behavior of loose, contractant granular assemblies, approaching the critical state for large $\epsilon _a$ , corresponds to the upper envelop of the stress-strain behaviour. Those events consist in $(i)$ a very fast (slip) part in which a drop of $q$ coincides with a jump of $\epsilon _v$ (contraction), while loss of control of $\epsilon _a$ and generation of pore pressure signal a dynamic collapse of the material structure triggered by an instability; and then $(ii)$ a quasi-static (stick) part in which the sample regains its strength and, over a short strain interval, behaves similarly to a denser system that dilates before reaching its critical state. A unique stress-dilatancy relation applies to all stick-slip events. Apparent internal friction angles and effects of strain rate and confining pressure are discussed, and it is argued that stick-slip instabilities originate in physico-chemical aging phenomena coupled to contact mechanics.     

Rheology of weakly wetted granular materials: a comparison of experimental and numerical data

Shear cell simulations and experiments of weakly wetted particles (a few volume percent liquid binders) are compared, with the goal to understand their flow rheology. Application examples are cores for metal casting by core shooting made of sand and liquid binding materials. The experiments are carried out with a Couette-like rotating viscometer. The weakly wetted granular materials are made of quartz sand and small amounts of Newtonian liquids. For comparison, experiments on dry sand are also performed with a modified configuration of the viscometer. The numerical model involves spherical, monodisperse particles with contact forces and a simple liquid bridge model for individual capillary bridges between two particles. Different liquid content and properties lead to different flow rheology when measuring the shear stress-strain relations. In the experiments of the weakly wetted granular material, the apparent shear viscosity $\eta _g$ η g scales inversely proportional to the inertial number $I$ I , for all shear rates. On the contrary, in the dry case, an intermediate scaling regime inversely quadratic in $I$ I is observed for moderate shear rates. In the simulations, both scaling regimes are found for dry and wet granular material as well.     

Double-walled carbon nanotubes under hydrostatic pressure: Raman experiments and simulations

We have used Raman spectroscopy to study the behavior of double-walled carbon nanotubes (DWNT) under hydrostatic pressure. We find that the rate of change of the tangential mode frequency with pressure is higher for the sample with traces of polymer compared to the pristine sample. We have performed classical molecular dynamics simulations to study the collapse of single (SWNT) and double-walled carbon nanotube bundles under hydrostatic pressure. The collapse pressure (pc) was found to vary as 1/R3, where R is the SWNT radius or the DWNT effective radius. The bundles showed approximately 30% hysteresis and the hexagonally close packed lattice was completely restored on decompression. The pc of a DWNT bundle was found to be close to the sum of its values for the inner and the outer tubes considered separately as SWNT bundles, demonstrating that the inner tube supports the outer tube and that the effective bending stiffness of DWNT, D(DWNT) - 2D(SWNT).     

Influence of relative density on granular materials behavior: DEM simulations of triaxial tests

The rheological behavior of non-cohesive soils results from the arrangement and complex geometry of the grains. Numerical models based on discrete element modeling provides an opportunity to understand these phenomena while considering the discrete elements with a similar shape to that of the grains the soil is composed of. However, dealing with realistic shapes would lead to a prohibitive calculation cost. In a macroscopic modeling approach, simplification of the discrete elements’ shape can be done as long as the model can predict experimental results. Since the intrinsic non-convex geometry property of real grains seems to play a major role on the response of the granular medium, it is thus possible to keep this geometrical feature by using cluster of spherical discrete elements, which has the advantage to reduce dramatically the computation cost. Since the porosities found experimentally could not always be obtained with the numerical model—owing to the huge difference in shape, the notion of relative density, which requires a search for minimum and maximum porosities for the model, was chosen to compare the experimental and numerical results. Comparing the numerical simulations with the experimental triaxial tests conducted with relative densities and different confining pressures shows that the model is able to predict the experimental results.     

Experimental and numerical determination of representative elementary volume for granular plant materials

A series of physical and numerical tests were conducted to determine representative elementary volume of granular plant material. The load response of pea grain assembly poured into a cuboid test chamber and subjected to uniaxial confined compression was studied. The apparatus was equipped with adjustable side walls that allowed measurement of boundary stresses in samples of varying thickness. It was found that load distribution varied considerably in samples of thickness smaller than three times the size of the particle. Less pressure variation was observed in grain assemblies of thickness equaled to three, five and seven times the particle size. Comparison between experimental data and numerical DEM results have shown qualitative agreement. It was found that the specimen of dimension not smaller than five times the particle size can be used as a representative elementary volume in confined uniaxial compression test of granular plant materials.     

Investigations on the linear friction welding process through numerical simulations and experiments

Linear Friction Welding (LFW) is a solid-state joining process applied to non-axisymmetric components. LFW involves joining of materials through the relative motion of two components undergoing an axial force. In such process the heat source is given by the frictional forces work decaying into heat determining a local softening of the material and eventually bonding conditions. In the paper the authors present a designed and assembled laboratory fixture for LFW operations and the results of an experimental and numerical campaign aimed to weld steel parts. The dedicated fixture permitted to highlight the effect of the most important process parameters. Process conditions allowing effective bonding conditions were highlighted and local conditions of pressure and temperature determining effective bonding of the specimens were determined.     

On the influence of inter-particle friction and dilatancy in granular materials: a numerical analysis

Mechanical behavior of granular soils is a classic research realm but still yet not completely understood as it can be influenced by a large number of factors, including confining pressure, soil density, loading conditions, and anisotropy of soil etc. Traditionally granular materials are macroscopically regarded as continua and their particulate and discrete nature has not been thoroughly considered although many researches indicate the macro mechanical behavior closely depends on the micro-scale characteristics of particles. This paper presents a DEM (discrete element method)-based micromechanical investigation of inter-particle friction effects on the behavior of granular materials. In this study, biaxial DEM simulations are carried out under both ‘drained’ and ‘undrained’ (constant volume) conditions. The numerical experiments employ samples having similar initial isotropic fabric and density, and the same confining pressure, but with different inter-particle friction coefficient. Test results show that the inter-particle friction has a substantial effect on the stress-strain curve, peak strength and dilatancy characteristics of the granular assembly. Clearly, it is noted that apart from the inter-particle friction, the shear resistance is also contributed to the dilation and the particle packing and arrangements. The corresponding microstructure evolutions and variations in contact properties in the particulate level are also elaborated, to interpret the origin of the different macro-scale response due to variations in the inter-particle friction.     

Failure of spheroplastics under axial tension and hydrostatic compression

The problem of determination of the external pressure and axial tensile force, which fail spheroplastics — a structurally inhomogeneous material consisting of hollow glass microspheres of different diameters, the latter being distributed in a random manner in a continuous epoxy matrix — is examined.Translated from Problemy Prochnosti, No. 9, pp. 59–61, September, 1990.     

Micro-mechanical behaviour of granular materials under gravity-induced stress gradient

Gravity-induced stress gradient plays an important role both in terrestrial and extra-terrestrial geotechnical engineering. Its effect on the behaviour of granular materials was studied by DEM simulations for the representative volume element under triaxial conditions. The shear strength and volumetric dilatancy decrease at first and then stabilizes with increasing stress gradient; the critical gravity shows a stress level-dependency. Corresponding micromechanics was further explored. The stress gradient restrains the original decrease in valence and the increase in elongation degree of void cells. The number of void cells oriented parallel to the loading direction is also decreased. All of the original increase tendencies of those micro-parameters are also significantly restrained by the stress gradient during triaxial loading. A stress level-dependent critical gravity was observed beyond which those micro-parameters stabilize. The stress gradient leads to significantly more particles participating in load-bearing both during isotropic compression and triaxial loading, and leads to a relative stable fraction of strong force chain in the latter tests. The stress gradient appears to have no significant influence on the spatial distribution of micro slip bands, but results in a stable area fraction. Meanwhile, their overall number is reduced, whilst the average length and width are generally increased. The effect of gravity on void cell fabrics physically originates from those gravity-sensitive particles which are poorly supported and have an acceleration mainly caused by the gravity. The gravity-sensitive evolution patterns of void cells were presented finally, which gives a good explanation for both the macroscopic and microscopic observations.