DEM investigation of particle anti-rotation effects on the micromechanical response of granular materials

The importance of particle rotation to the mechanical behavior of granular materials subject to quasi-static shearing has been well recognized in the literature. Although the physical source of the resistance to particle rotation is known to lie in the particle surface topography, it has been conveniently studied using the rolling resistance model installed typically on spherical particles within the DEM community. However, there has been little effort on assessing the capability of the rolling resistance model to produce more realistic particle rotation behavior as exhibited by irregular-shaped particles. This paper aims to eliminate this deficiency by making a comprehensive comparison study on the micromechanical behavior of assemblies of irregular-shaped particles and spherical particles installed with the rolling resistance model. A variety of DEM analysis techniques have been applied to elucidate the full picture of micromechanical processes occurring in the two types of granular materials with different particle-level anti-rotation mechanisms. Simulation results show that the conventional rheology-type rolling resistance models cannot reproduce the particle rotation and strain localization behavior as displayed by irregular-shaped materials, although they demonstrate clear effects on the macroscopic strength and dilatancy behavior, as have been adequately documented in the literature. More insights into the effects of particle-level anti-rotation mechanism are gained from an in-depth inter-particle energy dissipation analysis.     

Investigating the micromechanical evolutions within inherently anisotropic granular materials using discrete element method

This paper investigates the mechanical behavior of inherently-anisotropic granular materials from macroscopic and microscopic points of view. The study is achieved by simulating biaxial compression tests performed on granular assemblies by using numerical discrete element method. In the same category of numerical studies found in the literature, the simulations were performed by considering elliptical/oval particles. In the present study, however, the shape of particles is considered as convex polygons, which mostly resembles real sand grains. Particle assemblies with four different bedding angles were tested. Similar to what observed in experiment, inherent anisotropy has a significant effect on macroscopic mechanical behavior of granular materials. The shear strength and dilative behavior of assemblies were found to decrease as the bedding angle increases. Evolution of the microstructure of all samples and the influence of bedding angle on the fabric and force anisotropy during loading process were investigated. It is seen that the microscopic evolutions in the fabric can justify well the macroscopic behavior of granular assemblies. It is found that the long axis of particles tend to be inclined perpendicular to the loading axis, which results in generating more stable column-like microstructures in order to transfer the applied load. Moreover, the number of contacts as well as the magnitude of forces among particles varies in different directions during the loading process and the initial anisotropy condition totally evolves due to the induced anisotropy within samples.     

Experimental micromechanical evaluation of strength of granular materials: Effects of particle rolling

Biaxial compression tests have been performed on assemblies of oval cross-sectional rods, in an effort to evaluate the effects of interparticle friction, particle shape, and initial fabric on the overall strength of granular materials. The variation in the spatial arrangement of the particles (fabric) and particle rolling and sliding are monitored by taking photoelastic pictures at various stages during the course of deformation. Based on this, the following conclusions are obtained. (1) Particle rolling appears to be a major microscopic deformation mechanism, especially when interparticle friction is large. (2) There are relatively few contacts at which relative sliding is dominant, and this seems to be true even when the assembly reaches the overall failure state; this observation is in contradiction to the common assumption that particle sliding is the major microscopic deformation mode. (3) During the course of deformation and up to the peak stress, new contacts are continually formed in such a manner that the contact unit normals tend to concentrate more in a direction parallel to the maximum principal compression. This concentration of unit normals seems to be closely related to the formation of new column-like load paths which carry the increasing axial stress under constant lateral force. After the peak stress, such a column-like microstructure disappears and considerable rearrangement of the load paths takes place, leading to a more diffused (homogeneous) microstructure in the critical state. (4) If a fabric tensor F_ij, i, J = 1,2,3, is defined to be proportional to the volume average of the quantity m_im_j, where m_i are the rectangular Cartesian components of a unit vector along a vector that connects the centroids of two typical contacting granules, then it appears that the overall stress with components σ_ij tends to become coaxial with the fabric tensor F_ij, as the overall deformation continues. For two-dimensional granules the result σ_ij = _OF_ij + β_OF_jkF_kj (k summed) obtained by Mebrabadi, Nemat-Nasser and Oda (1980) by microchemical modeling is confirmed experimentally; _O and β_O are material parameters.     

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.     

On fluidization of polydisperse granular materials

A method has been developed for calculating the fractional composition of boiling bed particles liquefied at a given speed of filtration with account for the composition of the supplied granular materials. The relation between the maximum size of particles and their mean diameter and the degree of polydispersity has been investigated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 353–357, March–April, 2008.     

Development of micromechanical models for granular media

Micromechanical analysis has the potential to resolve many of the deficiencies of constitutive equations of granular continua by incorporating information obtained from particle-scale measurements. The outstanding problem in applying micromechanics to granular media is the projection scheme to relate continuum variables to particle-scale variables. Within the confines of a projection scheme that assumes affine motion, contact laws based on binary interactions do not fully capture important instabilities. Specifically, these contact laws do not consider mesoscale mechanics related to particle group behaviour such as force chains commonly seen in granular media. The implications of this are discussed in this paper by comparison of two micromechanical constitutive models to particle data observed in computer simulations using the discrete element method (DEM). The first model, in which relative deformations between isolated particle pairs are projected from continuum strain, fails to deliver the observed behaviour. The second model accounts for the contact mechanics at the mesoscale (i.e. particle group behaviour) and, accordingly, involves a nonaffine projection scheme. In contrast with the first, the second model is shown to display strain softening behaviour related to dilatancy and produce realistic shear bands in finite element simulations of a biaxial test. Importantly, the evolution of microscale variables is correctly replicated. This paper is dedicated to Professor Ching S. Chang on the occasion of his 60th birthday.     

Dense granular flow at the critical state: maximum entropy and topological disorder

After extensive quasi-static shearing, dense dry granular flows attain a steady-state condition of porosity and deviatoric stress, even as particles are continually rearranged. The paper considers two-dimensional flow and derives the probability distributions of two topological measures of particle arrangement—coordination number and void valence—that maximize topological entropy. By only considering topological dispersion, the method closely predicts the distribution of void valences, as measured in discrete element (DEM) simulations. Distributions of coordination number are also derived by considering packings that are geometrically and kinetically consistent with the particle sizes and friction coefficient. A cross-entropy principle results in a distribution of coordination numbers that closely fits DEM simulations.     

A semi-empirical re-evaluation of the influence of state on elastic stiffness in granular materials

Granular Matter - The calculation of the impact pressure on obstacles in granular flows is a fundamental issue of practical relevance, e.g. for snow avalanches impacting obstacles. Previous...     

Numerical analysis of critical state behaviors of granular soils under different loading conditions

Discrete element method is used to simulate granular assembly behaviors with different initial conditions under three different loading conditions—plain strain, conventional triaxial compression, and direct shear. Different deformation modes of specimens with different conditions are presented. Some important parameters of the critical state theory are investigated. Uniqueness of the critical state line is checked which shows that there is no a unique critical state line for specimens with different initial void ratios under different loading conditions. Frictional angles and dilation angles of specimens with different conditions at critical state are compared. Void ratios and coordination numbers of specimens at critical state are studied. Anisotropies of the particle orientation and normal contact force at initial state, critical state, as well as the evolutions during shearing are analyzed. The anisotropy is shown to have significant effects on the soil behaviors and is related to the non-uniqueness of the critical state line. The developed numerical models can be used to study the micromechanics and microstructure of the specimen subjected to different loading conditions in the future.     

On the critical size of microcracks initiated in materials

We obtain an explicit expression for the potential energy of an elastic body containing a crack with prefracture zones at its tips. This expression is used to construct an analytic dependence of the critical size of a microcrack required for its transformation into a macroscopic defect by using the theory of catastrophes. The reliability of the obtained theoretical values of the critical size of a microcrack is corroborated by comparing these results with the available experimental data. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 3, pp. 79–83, May–June, 1998.     

On distortion of tensor and yield criteria of granular materials

The distortion of tensor defined by use of normals on the tensor ellipsoid and the mean distortion are introduced. It is explained that the distortion represents the unit shear strain for the finite strain tensor, and the shear-normal stress ratio for the stress tensor. The spatial mobilized plane which plays a very important role in the mechanics of granular materials is regarded as a plane on which the distortion of stress tensor coincides with its mean distortion, and the yield criteria of granular materials are considered applying the concept of the distortion of stress tensor.     

Mixtures of granular materials

Balance laws are given for a mixture of granular materials of a type described by Goodman and Cowin. Constitutive equations are given for the case of two dry granular constituents, and consequences of the entropy principle are found.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.     

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.     

On random characteristics of composite materials

Abstract

Theoretical formulation is described, which presents random characteristics in composite materials. The presented method is based on Poisson processes. Examples of random characteristics of composite materials are shown. The method presented can be used for evaluation of composite materials and the subsequent quantitative stochastic design as well as stochastic optimisation of composite materials.