颗粒材料剪胀性的微观力学分析

剪胀性是颗粒材料在加载过程中表现出来的重要变形特性。以孔隙胞元描述颗粒材料内部结构的最小单元,通过对单个孔隙胞元进行剪切受力分析,探讨了剪切过程中颗粒材料体积的改变对应力比和单个孔隙胞元形状的依赖关系,解释了排列密实的颗粒材料在剪切过程中先压缩后剪胀的微观机制。用离散元数值模拟得到了在双轴剪切过程中单个孔隙胞元形状以及孔隙胞元体积变形的演化过程。离散元数值结果表明,加载过程中孔隙胞元形状由初始各向同性到沿大主应力方向变大变长、体积变形先压缩后膨胀,并且体积变形在加载过程中存在局部化现象,体积变化大的孔隙胞元在较大变形时,排列成倾斜的窄带。综合孔隙胞元的受力分析和离散元数值结果表明,致密排列颗粒材料的剪胀性与微观尺度上孔隙胞元的几何结构及其内部的力链传递方式密切相关。     

Instability and ill-posedness in the deformation of granular materials

A linear stability analysis of the partial differential equations of granular flow is performed. The constitutive relations include (i) elastic effects, (ii) non-associated flow rules and (iii) shear-strain hardening. Conditions for the equations to be well-posed and to be stable are derived. It turns out that there are two qualitatively different kinds of instability; which appears first depends on the parameters of the constitutive relations. If one kind appears first, then in a constitutive test a period of inhomogeneous deformation is predicted to occur before the formation of shear bands. If the other kind appears first, then shear bands are predicted to form in an approximately homogeneous sample. Some constitutive experiments are analysed from this viewpoint, and the analysis suggests some new experimental work.     

易破碎粒状材料本构研究

粒状材料被广泛地应用到土木工程的各个领域。大部分粒状材料在外力作用下较容易产生颗粒破碎,颗粒破碎对材料的力学性能有很大的影响。为了更好地描述易破碎粒状材料的力学特性,基于弹塑性力学和临界状态土力学开发了一种能够考虑颗粒破碎效应的本构模型。此本构模型能够考虑在剪应力和压应力作用下引起的颗粒破碎对粒状材料力学性能的影响。为了考虑颗粒破碎的影响,基于对Cambria 砂的高压试验,得出了临界状态线位置与消耗塑性功之间的关系,并称之为“破碎方程”。此本构模型拥有双屈服面,分别考虑剪切和等向压缩产生的塑性变形。通过试验结果与数值计算结果的对比得出,新的本构模型能较好地描述易破碎粒状材料的力学特性     

Plastic compaction of cemented granular materials

We analytically relate hydrostatic stress to strain in a random dense pack of identical spheres cemented at their contacts. The spheres are elastic and the cement is perfectly plastic. This solution for the sphere pack is based on a solution for the normal interaction of two cemented spheres. Initially, the two spheres touch each other at a point. We show that, as loading increases and cement becomes plastic, a finite (Hertzian) direct-contact area between the spheres necessarily has to develop and progress. The stress-strain behavior of the pack depends on the cement's yield limit and on the amount of cement. At the same hydrostatic stress, the deformation of the cemented aggregate is smaller than that of the uncemented one. This difference becomes large as the yield limit increases. We calculate the bulk modulus of an aggregate from the stress-strain curve. In the plasticity domain, the bulk modulus of the cemented aggregate is smaller than that of the uncemented one. The difference between the two may easily reach 50%. Of course, as the cement's yield limit decreases, the aggregate's stress-strain curve and the bulk modulus approach those of the uncemented sphere pack. This theoretical conclusion is qualitatively supported by experiments on epoxy-cemented glass beads. The maximum contact stress in the cemented aggregate may be less than a half of that in the uncemented one. This result explains an experiment where an uncemented glass bead sample failed at a hydrostatic stress of 50 MPa, whereas an epoxy-cemented sample stayed intact.     

A variational principle for granular materials

A major problem in the mathematical modelling of the deformation of granular materials has been the lack of an easily usable variational principle. This is because the frictional dissipation of energy in these materials does not allow the use of the classical extremum principles. In this paper, a variational principle is constructed which is valid even when frictional dissipation occurs. Its derivation uses results from the mathematical theory of envelopes. Both the stresses and the strains can be varied, and for the case of non-frictional plasticity it reduces to the maximum work principle of Hill. An example is presented to show how this new principle can be used to obtain approximate solutions to boundary-value problems with granular materials. The only requirements in advance are a displacement field that obeys the kinematic boundary conditions, and a stress field that obeys equilibrium and the static boundary conditions. The principle is therefore quite straightforward to apply.     

Vermiculate artefacts in image analysis of granular materials

Some reported analyses of images of deforming granular materials have generated surprising vermiculate strain features which are difficult to reconcile with the mechanics of deformation of granular matter. Detailed investigation using synthetic images and improved processing of images of laboratory experiments indicates that such features can emerge as a consequence of the image acquisition (sensor, contrast, resolution), the subsequent image correlation implementation, and the user’s choice of processing parameters. The two principal factors are: (i) the texture and resolution of the images and (ii) the algorithm used to achieve sub-pixel displacement resolution. Analysis of the images using a sub-pixel interpolation algorithm that is more robust than that used originally eliminates the vermiculate features for images with moderate resolution and texture. However, erroneous features persist in images with low resolution and poor texture. Guidance is provided on ways in which such artefacts can be avoided through improved experimental and image analysis techniques.     

颗粒接触力检测方法评述

颗粒物质是大量固体颗粒体系的集合体,其特性区别于普通固体和液体等物质的性质,颗粒物质基础力学问题的研究20年来一直是科学的前沿,从分析多尺度结构和相关物理机制的角度研究颗粒物质可能取得突破。首先介绍了微观尺度--亦即单颗粒尺度颗粒间接触力的检测方法,包括高精度电子天平称重法、显色灵敏复写纸压痕方法、光弹实验方法、荧光共聚焦显微镜法和磁共振弹性成像法等,根据检测过程中是否对颗粒带来影响划分为接触式检测和非接触式检测两大类,并对这些方法的工作原理、检测结果和优缺点进行了评述。我们指出接触式测量对颗粒体系带来了或多或少的干扰,特别是由于力链对局部力的变化反应极为敏感,轻微的变化足以使得力链结构发生很大变化,开展无干扰的光测实验是必然的发展趋势,而现阶段开展二维光弹性实验是很有意义的。最后介绍了作者正在进行的颗粒物质光弹力学实验的研究工作。     

Breakage and deformation mechanisms of crushable granular materials

Biaxial compressional tests with two types of stress paths were carried out on an assembly of round bars, which can be crushed to investigate the breakage and deformation mechanisms of granular materials at the mesoscale. The following was found experimentally: (1) upon loading, the crushable rods slide, rotate and break, and finally the breakage band forms for the two types of stress paths and different stress states; and (2) for the axial loading stress path, the round rods mainly fail in the vertically split mode and laterally crushed mode. However, for the lateral unloading stress path, the round rods fail with the combination mode of locally crushed and vertically split.     

粒状材料的强度与变形

颗粒破碎的特征表明,颗粒破碎具有分形特征,是影响粒状材料变形与强度的主要因素,根据颗粒破碎的分形模型可以建立粒状材料的变形与强度理论。假定粒状材料是均匀的D维分形体,由此导出粒状材料的抗张强度公式,并用来估算颗粒在给定压力下的破碎几率。颗粒破碎增加了单位体积颗粒的表面积,即颗粒的比表面能量增加,根据颗粒破碎过程中的能量守恒导出粒状材料一维压缩变形的表达式。     

Mechanical behaviour and failure of cohesive granular materials

We investigate the stress–strain behaviour and failure of a cohesive granular material both by experiments and numerical simulations. The material is an assembly of aluminium rods glued together by means of an epoxy resin. The behaviour of cohesive bonds (force–displacement relationship, failure conditions) is characterized by performing simple loading tests (tension/compression, shear…) on a couple of rods. Then, this local behaviour is introduced in a numerical code based on a discrete element method in order to perform numerical compression tests on large samples. The validation of this approach was the main goal of the present investigation that is essentially achieved by a direct comparison between the numerical results and similar experimental tests. As a basic application, we derive the macroscopic cohesion and friction characteristics of random cohesive materials by systematic numerical simulations in a biaxial geometry. Copyright © 2004 John Wiley & Sons, Ltd.     

On statistical description of stress and fabric in granular materials

The notion of overall macroscopic stress in granular masses is examined from a fundamental point of view by a statistical consideration of the contact forces that are transmitted by the contacting granules at the microscale. This examination leads in a natural way to relations between the macroscopic stress and the resulting granular fabric. The overall stresses are expressed in terms of the contact forces in two different but complementary ways: (1) by a statistical averaging over the sample volume of contact forces and “branches” which are vectors connecting the centroids of two contacting granules; and (2) by defining the overall tractions transmitted across an interior imagined plane as the sum of the contact forces which represent the mechanical effect of granules on one side of a unit area of this plane, upon those on the other side. Conditions under which the two representations of overall stresses are equivalent, are examined in detail. In addition, explicit results are given, which, define stresses in terms of the fabric and other microstructural characteristics of the granular mass.     

光弹颗粒材料的直剪实验研究

对颗粒材料中的力链分布特征的了解,有助于从根本上了解颗粒材料基本性质。借助光弹实验,对两种直径混合的颗粒材料在二维直剪作用下的平均强度力链分布和几何结构变化进行了初步的探索。光弹实验方法是目前能够直观观察到力链分布的唯一有效的实验方法,在进行光弹实验前,设计研制了光弹直剪仪并进行了多次光弹圆盘颗粒材料退火实验。利用数字图像技术对光弹实验结果进行处理,并尝试用彩色梯度算法表征颗粒材料的平均受力情况,并获得平均强度力链。结果表明,二元颗粒材料集合体的几何结构具有各向异性。对力链方向统计分析表明,平均强度力链出现了局部化。     

From solid to granular gases: the steady state for granular materials

This paper aims at extending the well‐known critical state concept, associated with quasi‐static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure‐imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlocal orientational distribution of contact forces in granular samples containing elongated particles

In this paper we introduce the branch tensor as an internal variable able to account for the structural anisotropy of a granular sample. The distribution of averaged contact forces is assumed to depend not only on the macroscopic stress and the local orientation, but also on the value of the fabric tensor. In contrast to previous work, including the fabric tensor has the crucial advantage that accounts for all relative positions between interacting particles, through the average value of the branch tensor. Based on a classical representation result, we propose an identification procedure that uses information obtained from both isotropic and anisotropic configurations.     

Statistical analysis of stress transmission in wet granular materials

The micromechanics of wet granular materials encompasses complex microstructural and capillary interconnects that can be readily described through a formal derivation of stress transmission in such a 3‐phase medium. In the quest for defining an appropriate stress measure, the stress tensor expression that results from homogenization [Duriez et al. J Mech Phys Solids 99 (2017): 495‐511] of such a medium provides theoretical insights necessary to extract useful information on the relationship between capillary effects and microforce interactions via several small‐scale parameters whose evaluation can be challenging. Using instead a statistical approach where microvariable distributions are described by probability density functions, the current study provides simple estimates of stress components in terms of only a few tractable microvariables such as coordination number and fabric anisotropy. In particular, the latter recognizes details of contacts such as force interactions being either mechanical or capillary, including interactions with and without mechanical contact. The developed expressions are in a good agreement with discrete element method simulation results of the triaxial loading of a wet granular assembly, notably for hydrostatic (mean) pressure. A new set of dimensionless groups is also identified to characterize the significance of mechanical and capillary physics, which facilitates a better understanding of the contribution of dominating elements to stress, while also providing the opportunity to incorporate important capillary effects in micromechanically based constitutive formulations.     

Finite element modelling of rate-dependent ratcheting in granular materials

The present paper introduces a comprehensive model that is capable of describing the behaviour, under cyclic loading, of the granular materials used in railway tracks and road pavement. Its main thrust is the introduction of the “Chicago” law in a continuum approach to account for the ratcheting effects. It also emphasizes rate-dependency as a dissipative mechanism that acts independently or jointly with the ratcheting effect as well as the non-associated plasticity. The numerical procedure is based on the return mapping algorithm, where Newton’s method is used to calculate the nonlinear consistency parameter of the flow rule and to obtain a consistent tangent modulus. The model was applied to specific numerical examples including multi-axial and cyclic loading conditions.     

Gradient plasticity modelling of strain localization in granular materials

The flow stress in the yield surface of plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain to model the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into the finite element code ABAQUS and used to simulate biaxial shear tests on dry sand. It is shown that the shape of the post-peak segment of the load displacement curve predicted by the numerical analysis is dependent on the mesh size when gradient term is not used. Use of an appropriate gradient coefficient is shown to correct this and predict a unique shape of the load displacement curve regardless of the mesh size. The gradient coefficient required turns out to be approximately inversely proportional to the mesh elemental area. Use of the strain gradient term is found to diffuse the concentration of plastic strains within shear band resulting in its consistent width. The coefficient of the higher gradient term appears as a function of the grain size, the mean confining stress, and the plastic softening modulus. Copyright © 2004 John Wiley & Sons, Ltd.     

Spatiotemporal analysis of strain localization in dense granular materials

Acta Geotechnica - Predicting localized failure in granular materials is a problem of great interest from both the scientific and technological perspectives. The initiation and growth of strain...     

A numerical representation of fracturing granular materials

This paper describes the computer algorithms used in a numerical simulation of the compression of an aggregate of crushable grains. It has been used in a model for the evolution of a granular medium under one-dimensional compression, in which the probability of fracture for individual particles is a function of applied stress, particle-size and co-ordination number. The information relating to the particles is represented in a compact way on the computer which allows the number of particles produced to become sufficiently large for satisfactory comparisons to be made with experimental data and which allows information, such as the positions and sizes of the particles, to be easily extracted. An algorithm based on the representation is used to locate neighbouring particles in a way which does not deteriorate unacceptably in terms of speed as the number of particles increases. © 1997 by John Wiley & Sons, Ltd.     

Three-dimensional discrete element method for granular materials

This paper describes a three-dimensional discrete element method of analysis for granular materials. Individual particles are modelled as rigid, six-sided solids with six degrees of freedom. Various types of contacts are possible among the three-dimensional discrete elements. Models for these contact types are described. Computational aspects of the method, such as techniques for contact detection and data structure, are addressed. Selective results of three examples that demonstrate the application of the method to granular flow problems are presented and discussed.