3D experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography

Many experimental studies have demonstrated that mechanical response of granular materials is highly influenced by micro-structural fabric and its evolution. In the current literature, quantification of fabric and its evolution has been developed based on micro-structural observations using Discrete Element Method or 2D experiments with simple particle shapes. The emergence of X-ray computed tomography technique has made quantification of such experimental micro-structural properties possible using 3D high-resolution images. In this paper, synchrotron micro-computed tomography was used to acquire 3D images during in-situ conventional triaxial compression experiments on granular materials with different morphologies. 3D images were processed to quantify fabric and its evolution based on experimental measurements of contact normal vectors between particles. Overall, the directional distribution of contact normals exhibited the highest degree of isotropy at initial state (i.e., zero global axial strain). As compression progressed, contact normals evolved in the direction of loading until reaching a constant fabric when experiments approached the critical state condition. Further assessment of the influence of confining pressure, initial density state, and particle-level morphology on fabric and its evolution was formed. Results show that initial density state and applied confining pressure significantly influence the fabric-induced internal anisotropy of tested specimens at initial states. Relatively, a higher applied confining pressure and a looser initial density state resulted in a higher degree of fabric-induced internal anisotropy. Influence of particle-level morphology was also found to be significant particularly on fabric evolution.     

A flow rule incorporating the fabric and non-coaxiality in granular materials

Deficiencies of constitutive models in prediction of dilatancy are often attributed to simplifications associated with flow rules such as assumptions of isotropy and coaxiality. It is thus proposed here to develop a comprehensive flow rule for granular materials by including the effect of fabric and without the assumption of coaxiality. A second-order tensor is introduced as a fabric for the distribution of contact normals and contact forces. By using the energy principle in micro-mechanical scale and a suitable dissipation mechanism in granular materials, a stress-dilatancy relation is obtained. Fabric plays a “bridge-like” role in the dilatancy and non-coaxiality. Non-coaxialities between stress-strain-fabric are attributed to the non-coaxiality between stress-fabric and strain-fabric. In this formulation the constants for modeling fabric depend on non-coaxiality of the system rather than the history that determines such a state. Ability of this stress-fabric-dilatancy for modeling the non-coaxiality shows that this relation can predict the behavior of granular materials in the presence of the rotation of principal stress axes.     

Macroscopic model with anisotropy based on micro–macro information

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by means of numerical simulations, we analyze dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy. The particle samples are first isotropically compressed and then quasi-statically sheared under constant volume (undrained conditions). From various static, relaxed configurations at different shear strains, infinitesimal strain steps are applied to “measure” the effective elastic response; we quantify the strain needed so that no contact and structure rearrangements, i.e. plasticity, happen. Because of the anisotropy induced by shear, volumetric and deviatoric stresses and strains are cross-coupled via a single anisotropy modulus, which is proportional to the product of deviatoric fabric and bulk modulus (i.e., the isotropic fabric). Interestingly, the shear modulus of the material depends also on the actual deviatoric stress state, along with the contact configuration anisotropy. Finally, a constitutive model based on incremental evolution equations for stress and fabric is introduced. By using the previously measured dependence of the stiffness tensor (elastic moduli) on the microstructure, the theory is able to predict with good agreement the evolution of pressure, shear stress and deviatoric fabric (anisotropy) for an independent undrained cyclic shear test, including the response to reversal of strain.     

Stress-chain based micromechanics of sand with grain shape effect

The mechanical behaviors of granular media are controlled by grain properties and microstructure. The primary property of granular media is denoted by its grain shape, grain size distribution, stiffness, and interparticle friction. The grain shape itself is of particular importance. Microstructures are formed in the connection paths of contact points between grains. In this paper, the deformation of granular materials with different grain shapes was simulated using two-dimensional DEM under different stress-levels and densities. After analyzing the results, the authors investigated fabric changes. The evolution rule of stress-induced anisotropy and its limitation as well as the existence of a critical state of fabric are revealed.     

Anisotropy of elasticity and fabric of granular soils

Anisotropy of elasticity is a very important feature of granular soils. In this paper, numerical experiments using discrete element method were performed to emulate drained triaxial tests and simple shear tests at different stress levels. From these numerical experiments the macroscopic elasticity parameters were determined. The results show that at isotropic stress states the stiffness of the numerical specimen increases, while the Poisson’s ratio decreases with increasing confining pressure. The small strain shear modulus of the numerical specimen agrees well with the laboratory experimental results on a specimen with similar conditions. At anisotropic stress states, there is a threshold stress ratio (\({ SR}_{\mathrm{th}}\)), which characterizes the degrees of stiffness change and fabric change during the shearing. When the stress ratio (SR) is less than \({ SR}_{\mathrm{th}}\), the microscopic contact number does not change and its distribution remains nearly isotropic, while the distribution of contact forces change and become anisotropic to resist the applied anisotropic stress. Therefore the stiffness anisotropy of the specimen mainly results from the anisotropy of contact forces. When SR is larger than \({ SR}_{\mathrm{th}}\), however, the contact number decreases significantly in the minor principal stress direction resulting in the fabric anisotropy, along with the adjustments of contact forces. The stiffness anisotropy of the specimen results from both the fabric anisotropy and the contact force anisotropy. It also indicates that the stress normalized stiffness may be used as an index of the degree of fabric anisotropy. Moreover, the Poisson’s ratio of the specimen increases continuously with increasing stress ratio and its anisotropy can be approximately related to the stiffness anisotropy.     

Fabric,force and strength anisotropies in granular materials: a micromechanical insight

In micromechanics, the stress–force–fabric (SFF) relationship is referred to as an analytical expression linking the stress state of a granular material with microparameters on contact forces and material fabric. This paper employs the SFF relationship and discrete element modelling to investigate the micromechanics of fabric, force and strength anisotropies in two-dimensional granular materials. The development of the SFF relationship is briefly summarized while more attention is placed on the strength anisotropy and deformation non-coaxiality. Due to the presence of initial anisotropy, a granular material demonstrates a different behaviour when the loading direction relative to the direction of the material fabric varies. Specimens may go through various paths to reach the same critical state at which the fabric and force anisotropies are coaxial with the loading direction. The critical state of anisotropic granular material has been found to be independent of the initial fabric. The fabric anisotropy and the force anisotropy approach their critical magnitudes at the critical state. The particle-scale data obtained from discrete element simulations of anisotropic materials show that in monotonic loading, the principal force direction quickly becomes coaxial with the loading direction (i.e. the strain increment direction as applied). However, material fabric directions differ from the loading direction and they only tend to be coaxial at a very large shear strain. The degree of force anisotropy is in general larger than that of fabric anisotropy. In comparison with the limited variation in the degree of force anisotropy with varying loading directions, the fabric anisotropy adapts in a much slower pace and demonstrates wider disparity in the evolution in the magnitude of fabric anisotropy. The difference in the fabric anisotropy evolution has a more significant contribution to strength anisotropy than that of force anisotropy. There are two key parameters that control the degree of deformation non-coaxiality in granular materials subjected to monotonic shearing: the ratio between the degrees of fabric anisotropy and that of force anisotropy and the angle between the principal fabric direction and the applied loading direction.     

Discrete element method investigation on thermally-induced shakedown of granular materials

Temperature change, as a common kind of internal perturbation performed on granular materials, has a significant effect on the bulk properties of granular materials. However, few studies on thermally-induced shakedown under a long-term thermal cycling were reported. In this work, the discrete element method was used to give insight into the thermally-induced shakedown on the fabric and stress states within non-cohesive, frictional granular assemblies. Assemblies were submitted to thermal cycling at a stationary boundary condition after experiencing a one-dimensional compression. Evolution of coordination number, entropy and anisotropy was investigated as well as boundary forces and contact forces. At the same time, effects of the heating rate, the initial vertical load and the magnitude of temperature change were examined. It demonstrates that thermal cycling induces a significant force relaxation within granular materials, while the corresponding granular fabric has a small change. In addition, the entropy and anisotropy decreases with thermal cycling. Moreover, the initial vertical load can constrain the development of thermally-induced fabric change, thereby limiting force relaxation to some degree. Both high heating rate and larger magnitudes of temperature change contribute to more significant force relaxation. However, they cause smaller fabric changes even though they provide larger perturbations.     

Effect of hybrid woven fabrics structure on their electrical properties

The aim of this study is to investigate the influence of hybrid textile woven fabric structure on the electrical resistivity. Weave structure was varied by varying the weave pattern and the conductive yarn density in the woven fabrics. Electrical surface and volume resistivity were measured and compared to the fabric structural properties. Results showed that not only the conductive yarns percentage has an important effect on the electrical resistivity but also the weave structure. The most influencing structural parameter on surface resistivity was the woven fabric surface profile as it controls the contact quality between the conductive yarns and the measuring electrodes. A high surface resistivity was noticed when the contact quality was poor. When this contact quality was good, a linear correlation was found between surface electrical resistivity and the cover firmness factor, the apparent conductive fiber surface area as well as the conductive yarn floating length of the woven structures.     

On micromechanical characteristics of the critical state of two-dimensional granular materials

In micromechanics of quasi-static deformation of granular materials, relationships are investigated between the macro-scale, continuum-mechanical characteristics, and the micro-scale characteristics at the particle and interparticle contact level. An important micromechanical quantity is the fabric tensor that reflects the distribution of contact orientations. It also contains information on the coordination number, i.e. the average number of contacts per particle. Here, the focus is on characteristics of the critical state in the two-dimensional case. Critical state soil mechanics is reviewed from the micromechanical viewpoint. Two-dimensional discrete element method (DEM) simulations have been performed with discs from a fairly narrow particle-size distribution. Various values for the interparticle friction coefficient and for the confining pressure have been considered to investigate the effect of these quantities on critical state characteristics (shear strength, packing fraction, coordination number and fabric anisotropy). Results from these DEM simulations show that a limiting fabric state exists at the critical state, which is geometrical in origin. The contact network tessellates the assembly into loops that are formed by contacts. For each loop, a symmetrical loop tensor is defined, based on its contact normals. This loop tensor reflects the shape of the loop. An orientation is associated with each loop, based on its loop tensor. At the critical state, the frequencies with which loops with different number of sides occur depend on the coordination number. At the critical state, these loops have, on average, the following universal characteristics, i.e. independent of the coordination number: (1) loops with the same number of sides and orientation have identical anisotropy of the loop tensor, (2) the anisotropy of the loop tensor depends linearly on the number of sides of the loop, (3) the distribution of loop orientations is identical, (4) Lewis’s law for the loop areas, which is a linear relation between the number of sides of loops and their area, is satisfied (not exclusively at the critical state) and (5) the areas of the loops do not depend on their orientation.     

Dry friction characterisation of carbon fibre tow and satin weave fabric for composite applications

Composites forming processes such as resin transfer moulding (RTM) typically involve a preforming step in which dry fabric material is deformed. Frictional forces in tool–fabric and fabric–fabric contacts determine the fabric deformation behaviour to a large extent. Previous investigations of the frictional behaviour of fibrous materials were mostly performed on a particular scale, i.e. microscopic (filament), mesoscopic (tow), or macroscopic (fabric). This study aims to provide a coupling between these scales by means of friction experiments on both carbon tows and carbon fabric in contact with metal counterfaces. The frictional behaviour of both materials on metal was measured on a capstan and a flat plate-friction setup. The frictional behaviour of fabric was comparable to that of single tows for matching pressures based on the mesoscopic contact area with the metal counterface. Furthermore, the agreement of the results forms a validation of both friction characterisation methods.     

纤维织物FEM-SPH耦合单胞模型及超高速碰撞特性

目前,对纤维织物超高速碰撞过程中的变形、断裂、破碎等力学行为已有较广泛的研究,但对碰撞过程中纱线间接触问题的分析尚未见公开文献报道。考虑纱线间的相互作用,建立了纤维织物的FEM-SPH耦合单胞模型,该模型不仅能够进行纤维织物超高速碰撞过程中的穿孔断裂、破碎、碎片云扩展等损伤行为分析,还能够进行纱线间的接触作用过程分析。结果表明,该模型分析结果与试验结果具有较好的一致性。      

Surface functionalization of silk fabric by PTFE sputter coating

This paper describes the surface functionalization of woven silk fabric by magnetron sputter coating of PTFE (polytetrafluoroethylene). The PTFE sputter coating was applied to improve the hydrophobic property of silk fabric. The effects of PTFE sputter coating on surface morphology and surface chemical properties were characterized using atomic force microscopy (AFM) and ATR-FTIR (attenuated total reflection-Fourier transform infrared spectroscopy). The wettability of the fabric was characterized through measuring the surface contact angle by a dynamic sessile analysis (DSA) technique. The contact angle of the PTFE coated fabric showed a significant increase from 68° to about 138°. The experimental results also revealed that larger sputtering pressures brought less contact angle hysteresis.     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.     

Modeling and preparation of a super-oleophobic non-woven fabric

A super-oleophobic surface has been achieved by satisfying two conditions: a properly designed surface morphology and a low surface energy. A meta-stable Cassie–Baxter model has been used to account for the super-oleophobic effect with a truly random rough surface such as hydro-entangled non-woven fabric. In this model, a high contact angle is obtained by a minimum of surface energy due to air pockets inside the rough structure. Apparent dodecane contact angles of greater than 150° were measured on a hydro-entangled, non-woven nylon fabric whose fibers had been modified using a pulsed plasma discharge containing 1H,1H,2H,2H-perfluorodecylacrylate (PFAC8). Good agreement between the predicted and measured contact angles was obtained using the meta-stable Cassie–Baxter model.     

三维连续体结构仿生拓扑优化新方法

Wolff法则是指骨骼通过重建/生长,保证骨小梁方向趋于与主应力方向一致以不断地适应它的力学环境。根据Wolff法则,建立了一种新的拓扑优化的准则法。该方法的基本思想是:(1)将待优化的结构看作是一块遵从Wolff法则生长的骨骼,骨骼的重建过程作为三维连续体结构寻找最优拓扑的过程;(2)用构造张量描述正交各向异性材料的弹性本构;(3)重建规律为结构中材料的更新规律。通过引入参考应变区间,材料更新规律可解释为:设计域内一点处主应变的绝对值不在该区间时,该点处构造张量出现变化;否则,构造张量不变化,该点处于生长平衡状态。(4)当设计域内所有点都处于生长平衡状态时,结构拓扑优化结束。采用各向同性本构模型,即令二阶构造张量与二阶单位张量成比例,分析三维结构拓扑优化。实例进一步验证基于Wolf法则的连续体结构优化方法的正确性和可行性。     

复合材料三维四向矩形编织物角柱结构研究

针对有限元计算对几何数据的需要,详细研究了由四步1∶1法编织的复合材料三维四向矩形编织物的角柱结构,为其建立了准确的几何模型。以矢量方法导出纺纱(纤维束)角柱段轴线、以及角柱段与内部段、角柱段与角柱段的接触线等的数学表达式。据此得到角柱结构几何参数值,它们可用于该材料的图形显示和力学分析。      

Detachment spectroscopy of metastable excitations in helium nanodroplets

Metastable states of helium nanodroplets in a beam are produced by electron impact and after several milliseconds are probed by a transverse light beam. Absorption of infrared photons by the excited droplets leads to the release of metastable triplet He*₂ molecules. These are subsequently detected when they eject electrons upon reaching a surface. By this method we can study the rotational structure of the absorption lines and infer the rotational state distribution of the molecules while in contact with the clusters. The results are rather surprising, and suggest that only the high J states and the J = 1 state of the molecule are populated.This work has been supported by the NSF through grants DMR9217525 and INT9311907.     

Quantum chemical calculation of electron transfer at metal/polymer interfaces

Calculation of contact charging at metal/polymer interfaces were performed by a quantum chemical method (DV-Xa). In the calculation, model clusters with dangling bonds were used. The model clusters showed surface states in the density of states (DOS), the electron transfer occurred at the contact interfaces between polymer and Al. Then, 0.3 nm was a reasonable value as the contact distance in the present simulation.Contact electrifications between PTFE and six metals, such as Pt, Au, Cu, Al, Pb and Ca were simulated. The charge transferred from the metal to PTFE depended on the work function of the metals, and had a gap in range of 4.25–4.28 eV. According to the gap of metals were classified into two groups. If Fermi level of a metal is lower than the lowest unoccupied molecular orbital (LUMO) level of PTFE, the electrons of the metal transfer to the surface state (interface state). Electrons in the other metals with a higher Fermi level move into the conduction band of PTFE.