Model For Granular Materials Research Articles

DEM investigation of the effect of intermediate principle stress on particle breakage of granular materials

This study investigates the influence of the intermediate principle stress on the particle breakage of granular materials. The crushable agglomerate method is applied to model soil particles and numerical true triaxial tests were carried out. The results show that particle breakage increases with increasing b value, the relationship of which follows an exponential function and agrees well with previous experimental results. More importantly, the study found that the relationship between particle breakage and total energy input is independent of the intermediate principle stress, which provides a good basis for the constitutive modeling of granular materials.

Snow avalanche friction relation based on extended kinetic theory

Abstract. Rheological models for granular materials play an important role in the numerical simulation of dry dense snow avalanches. This article describes the application of a physically based model from the field of kinetic theory to snow avalanche simulations. The fundamental structure of the so-called extended kinetic theory is outlined and the decisive model behavior for avalanches is identified. A simplified relation, covering the basic features of the extended kinetic theory, is developed and implemented into an operational avalanche simulation software. To test the obtained friction relation, simulation results are compared to velocity and runout observations of avalanches, recorded from different field tests. As reference we utilize a classic phenomenological friction relation, which is commonly applied for hazard estimation. The quantitative comparison is based on the combination of normalized residuals of different observation variables in order to take into account the quality of the simulations in various regards. It is demonstrated that the extended kinetic theory provides a physically based explanation for the structure of phenomenological friction relations. The friction relation derived with the help of the extended kinetic theory shows advantages to the classic phenomenological friction, in particular when different events and various observation variables are investigated.

Experiments and simulations of empty and sand-filled aluminum alloy panels subjected to ballistic impact

In this study, we use a discrete particle method in combination with finite element analysis to describe the interaction between structures and granular media during ballistic impact. By applying a discrete particle method to model granular materials, issues like mesh distortion and element deletion can be avoided. This paper presents experiments and numerical simulations on the perforation of empty and sand-filled aluminum alloy panels subjected to impacts by small-arms bullets. The simulations of the sand-filled panels were conducted using a combined discrete particle–finite element approach that accounts for the coupling between structure and sand. The ballistic capacity of the sand-filled aluminum panels was more than 40% higher than that of the empty aluminum panels. Overall, the results from the numerical simulations describe the trends from the experiments. The predicted ballistic capacity of the empty panels was within 5% of the experimentally determined value and the critical velocity of the sand-filled panels was predicted within 11% of the experimentally determined critical velocity. The scatter in residual velocity was similar in simulations and experiments. However, in its current form the discrete particle method needs different calibrations for different velocity regimes to obtain accurate description of the sand behavior.

Granular contact dynamics with elastic bond model

This paper proposes an elastic bond model in the framework of contact dynamics based on mathematic programming. The bond model developed in this paper can be used to model cemented materials. The formulation can be reduced to model pure static problems without introducing any artificial damping. In addition, omitting the elastic terms in the objective function turns the formulation into rigid bond model, which can be used for the modeling of rigid or stiffly bonded materials. The developed bond model has the advantage over the explicit DEM that large time step or displacement increment can be used. The tensile and shear strength criteria of the bond model are formulated based on the modified Mohr–Coulomb failure criterion. The torque transmission of bonds is introduced based on rolling resistance model. The loss of shear or tensile strength, or torque transmission will lead to the breakage of bonds, and turn the bond into purely frictional contact. Three simple examples are first used to validate the bond model. Numerical examples of uniaxial and biaxial compression tests are used to show its potential in modeling cemented geomaterials. Numerical results show that elastic bonds are indeed necessary for the modeling of cemented granular material under static conditions.

Energy-less strain in granular materials – Micromechanical background and modeling

During the macroscopic deformation of granular materials, which consist of an assembly of particles, the micromechanical structures change by forming new contacts or losing existing contacts. Among touching and non-touching particles in granular materials, touching particles contribute to macroscopic stress, which is given as the tensorial average of the contact forces between the particles. However, both touching and non-touching particles contribute to macroscopic strain, which is given by the tensorial average of the relative displacements between the particles. As non-touching particles lack contact force and contribute to no internal work, a constraint condition must be imposed on the macroscopic strain due to the non-touching particles; the work induced by the strain due to the non-touching particles must be zero. The strain that meets this constraint condition is called energy-less strain and it is studied further for applications to the macroscopic constitutive modeling of granular materials. The framework of the strain space multiple mechanism model is used to upscale the micromechanical structure of granular materials into the macroscopic constitutive modeling. Through this framework of study, the volumetric strain of the energy-less strain is identified as the dilative component of dilatancy in granular materials. The evolution of induced anisotropy, in terms of the fabric of the energy-less strain, is also identified.

Fabric rates applied to kinematic models: evaluating elliptical granular materials under simple shear tests via discrete element method

This study aims to identify a simple and accurate fabric rate to represent an angular velocity variable in a kinematic model of non-coaxial granular materials via discrete element method (DEM). The fabric tensor is a statistical quantity that represents vector directions (e.g., particle orientation, contact normal, contact force), the fabric anisotropy is an invariant of the fabric tensor which describes the vector direction anisotropy in an assembly, and the fabric inclination marks the principal direction of the fabric tensor—fabric rates are their respective time derivatives. Specimens with inherent anisotropy composed of elliptical particles were generated and tested using an upgraded two-dimensional (2D) DEM code, NS2D; naturally, it is appropriate to utilize a 2D DEM approach to investigate a 2D kinematic model. Strain-rate controlled constant-volume DEM monotonic and cyclic simple shear tests were conducted on two types of granular materials with particle aspect ratios of 1.4 and 1.7, and several fabric anisotropy rates and fabric inclination rates were considered based on a few fabric tensors: contact normal, contact force, and particle orientation. We then compared the theoretical rotation rates and measured fabric rates for a medium-dense specimen by DEM simple shear testing, and found that all the fabric anisotropy rates (and most fabric inclination rates) differed significantly from the theoretical values. Only the modified fabric inclination rate of particle orientation (FIRP) accurately reflected its theoretical rotation rate in the simple shear tests. Averaged micro-pure rotation rate (APR) was also applied to examine the rotation rates, as suggested by previous researchers, to explore the difference between APR as a statistical variable of time derivative of particle directions while FIRP is the time derivative of a statistical variable of particle directions.

Cutoff nonlinearities in the low-temperature vibrations of glasses and crystals.

We present a computer simulation study of glassy and crystalline states using the standard Lennard-Jones interaction potential that is truncated at a finite cutoff distance, as is typical of many computer simulations. We demonstrate that the discontinuity at the cutoff distance in the first derivative of the potential (corresponding to the interparticle force) leads to the appearance of cutoff nonlinearities. These cutoff nonlinearities persist into the very-low-temperature regime thereby affecting low-temperature thermal vibrations, which leads to a breakdown of the harmonic approximation for many eigenmodes, particularly for low-frequency vibrational modes. Furthermore, while expansion nonlinearities which are due to higher order terms in the Taylor expansion of the interaction potential are usually ignored at low temperatures and show up as the temperature increases, cutoff nonlinearities can become most significant at the lowest temperatures. Anharmonic effects readily show up in the elastic moduli which not only depend on the eigenfrequencies, but are crucially sensitive to the eigenvectors of the normal modes. In contrast, those observables that rely mainly on static structural information or just the eigenfrequencies, such as the vibrational density of states, total potential energy, and specific heat, show negligible dependence on the presence of the cutoff. Similar aspects of nonlinear behavior have recently been reported in model granular materials, where the constituent particles interact through finite-range, purely repulsive potentials. These nonlinearities have been ascribed to the nature of the sudden cutoff at contact in the force law. As a consequence, we demonstrate that cutoff nonlinearities emerge as a general feature of ordered and disordered solid state systems interacting through truncated potentials.

Meso-scale framework for modeling granular material using computed tomography

Numerical modeling of unconsolidated granular materials is comprised of multiple nonlinear phenomena. Accurately capturing these phenomena, including intergranular forces and grain deformation, depends on resolving contact regions several orders of magnitude smaller than the grain size. Here, we investigate a method for capturing the morphology of the individual particles using computed X-ray tomography, which allows for accurate characterization of the interaction between grains. Additionally, the ability of these numerical approaches to determine stress concentrations at grain contacts is important in order to capture catastrophic splitting of individual grains, which has been shown to play a key role in the plastic behavior of the granular material on the continuum level. Samples of Ottawa sand are numerically modeled under one-dimensional compression loadings in order to determine the effect of discretization approaches, such as mesh refinement, on the resulting stress concentrations at contact points between grains. The effects of grain coordination number and finite element type selection on these stress concentrations are also investigated.

Development of a New Mechanistic Empirical Rutting Model for Unbound Granular Material

AbstractThis paper proposes a new mechanistic-empirical rutting (MER) model to evaluate the permanent deformation (PD) behavior of unbound granular material (UGM). To characterize the stress dependence of rutting behavior in UGM, the MER model incorporated a softening stress term and a hardening stress term into the Tseng-Lytton model, which is based on the Drucker-Prager plastic yield criterion. Repeated load triaxial tests were performed on two types of UGMs in this study, employing seven stress states to calibrate the model coefficients, and two stress states to validate the accuracy of the model predictions. The correlations of the two incorporated stress terms with the accumulated permanent strains were established based on the triaxial test results. It was found that the correlations are fitted by power functions with 0.97–0.99 R2 values. The proposed MER model was compared with the existing UGM rutting models, including the MEPDG model, Korkiala-Tanttu model, and UIUC model in terms of differences ...

A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.

Unexpected collapses during isotropic consolidation of model granular materials

Abstract This paper reports the unexpected instantaneous instabilities of idealized granular materials under simple isotropic drained compression. Specimens of monosized glass beads submitted to isotropic compression exhibit a series of local collapses under undetermined external stress with partial liquefaction, experience sudden volumetric compaction and axial contraction of various amplitude. Short-lived excess pore water pressure vibrates like an oscillating underdamped system in the first dynamic transient phase and rapidly disperses in the subsequent longer dissipation phase. However, very dense samples maintain a collapse-free behaviour below a threshold void ratio e 30 col at 30 kPa of stress. The potential mechanisms that could explain these spontaneous collapses are discussed.

Historical Origin and Recent Development on Normal Directional Impact Models for Rigid Body Contact Simulation: A Critical Review

The impact is one of the most abundant phenomena in the field of multi-body dynamics when two or more bodies come in close vicinity and depending on the interaction properties and geometry, all the interacting bodies experience certain impulsive force for an infinitesimal duration. Nowadays, impact modelling becomes an intrinsic part in the modelling of structural pounding, granular materials, crash and machinery analysis, robotics and bio-mechatronics applications. Since the time of Newton, numerous literatures have been published on the modelling of both normal and oblique contact phenomena. The scope of this critical review is limited to consolidate the existing knowledge on the computational model of normal directional impact on rigid bodies. The literature related to modelling of oblique impact, soft body impact, impact damage in composites and associated stress wave propagation are excluded from the scope of this critical review. Smooth and non-smooth mechanics are two schools of thought in simulating the normal directional impact. In this review, the shortcomings of all the classes of compliance and non-smooth models are analysed in the unified dimensionless frame-work to compare their response output with the conventional stereo-mechanical model. This review opens a new avenue for future researchers in selecting a proper contact formulation for specific application.

Modeling of unsaturated granular materials in flexible pavements

The unsaturated granular material (UGM) is found to exhibit the moisture-sensitive and stress-dependent nonlinear cross-anisotropic behaviour in flexible pavements. This paper aims at developing a finite element (FE) model for pavement structure, which takes into account this behaviour of UGM. First, the Lytton model is employed to characterize the moisture-sensitive and stress-dependent behaviour of UGM, which incorporated a matric suction term to the existing stress-dependent constitutive model. The Lytton model is validated by the laboratory resilient modulus tests on the selected UGMs at different moisture contents. Second, the nonlinear cross-anisotropic constitutive equation of UGM is derived from the generalized Hooke’s Law. The coefficients of the constitutive model are determined by the rapid triaxial test. Third, a User-Defined Material (UMAT) subroutine is developed to characterize this constitutive behaviour in the FE software ABAQUS. The UMAT subroutine adopts the secant stiffness approach with multiple damping factors. The UMAT subroutine is then implemented in the FE model of flexible pavement structures. The FE simulation results indicate the nonlinear cross-anisotropic model predicts greater pavement responses than the isotropic model. When the UGM is suction sensitive, it is found that the moisture content of UGM significantly affects the moduli distribution of base layer and the critical strains (i.e., tensile strain at the bottom of asphalt concrete, and compressive strains in base and subgrade layers) of pavement structures.

Review on Thermo-mechanical Approach in the Modelling of Geo-materials Incorporating Non-associated Flow Rules

Recently, there has been a burgeoning interest in developing constitutive soil models from the laws of thermodynamics, mainly due to the benefits that these models automatically obey them and the approach provides a well-established structure and reduces the need for ‘ad hoc’ postulates. A thermodynamic framework, also known as thermo-mechanical framework, has the capability to predict the behaviour of geotechnical materials, which requires the anticipated incorporation of non-associated flow rules. As it is very challenging to achieve acceptable accuracy in plasticity modelling of granular materials, this paper aims to review this framework not only to discuss the details of the major components but also to highlight the capability of generating non-associated flow rules in a natural way from thermo-mechanical principles. This approach introduces the use of internal variables to develop the two thermodynamic potentials (the free energy and the rate of dissipation functions), sufficient to derive the corresponding yield function, flow rule, isotropic and kinematic hardening rules as well as the basic elasticity law. It is shown that the non-associated flow rule can be derived naturally from the postulated stress-dependent dissipation increment function. Comparison has been made with stress-independent dissipation to demonstrate that the approach can also successfully explain the behaviour of standard materials with associated flow rules. The basic steps for the thermo-mechanical formulation for developing a constitutive model are also reviewed and summarised. Furthermore, the power of conventional mathematical technique, Legendre transformation, in the derivation of constitutive equations has been highlighted.

A micro‐mechanical study of peak strength and critical state

SummaryWe present a micro‐mechanical analysis of macroscopic peak strength, critical state, and residual strength in two‐dimensional non‐cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain‐scale counterparts (e.g., inter‐particle contact forces, fabric, particle displacements, and velocities), providing an across‐the‐scale basis for a better understanding and modeling of granular materials. These multi‐scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain‐scale mechanics are established. Second, these relations are used in conjunction with the non‐associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro‐mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro‐mechanical conditions for peak strength, critical state, and residual strength. Copyright © 2015 John Wiley & Sons, Ltd.

Editorial: Modelling and computational challenges in granular materials

This is the editorial for the special issue on “Modelling and computational challenges in granular materials” in the journal on Computational Particle Mechanics (CPM). The issue aims to provide an opportunity for physicists, engineers, applied mathematicians and computational scientists to discuss the current progress and latest advancements in the field of advanced numerical methods and modelling of granular materials. The focus will be on computational methods, improved algorithms and the modelling of interesting industrial and academic problems.

Asymmetry of the stress tenor in granular materials

One of the basic assumptions of the micropolar theory is that the stress tensor is not symmetric. In this paper, asymmetry of the stress tensor is studied with discrete element method and averaging method. The change of the skew symmetric part of an asymmetric tensor with the rotation of the coordinate system is shown graphically. Averaging method is used to obtain stress tensor from a DEM simulation of biaxial test. Stress asymmetries at different locations, scales and time steps are studied. The importance of the asymmetric stress for setting up a constitutive model for granular materials is discussed.

Investigation of the effective elastic parameters in the discrete element model of granular material by the triaxial compression test

The general objective of the present paper is to improve the understanding of micromechanical mechanisms in granular materials and their representation in numerical models. Results of numerical investigations on micro–macro relationships in the discrete element model of granular material are presented. The macroscopic response is analysed in a series of simulations of the triaxial compression test. The numerical studies are focused on the influence of microscopic parameters on the initial response. The effect of the contact stiffness and friction coefficient on the effective elastic moduli is investigated. Numerical results are compared with the analytical estimations based on the kinematic Voigt's hypothesis as well as with selected numerical results of other authors. The comparisons show that a better agreement between the numerical and analytical results is observed for particle assemblies with higher coordination numbers. Higher coordination numbers are related to more compact specimens and for a given specimen can be associated with low values of the contact stiffness and a higher confining pressure.

The existence and convergence of the Maxwell model for granular materials

In this paper, we study the pseudo-Maxwell model for granular materials, we prove the existence of a solution to this model. Under some hypotheses on the initial data, for all time , the solution belongs to Schwartz’s space of rapidly decreasing smooth functions. In addition, we prove that the solution converges exponentially to the steady state when in some Sobolev space .

Numerical analysis of plastic behavior of granular media exposed to deformation under broken path loading

Based on DEM, the problem on uniform shearing of granular material specimen is considered, the shape of the particles was chosen to be spherical, with assigned distribution per radii. At interfaces of the particles, dry friction and viscosity were taken into account. Loading was implemented as simple and broken trajectory shearing. The load trajectory was broken by means of sudden change in the shearing direction. It has been found that in this case, dilatancy rate and angle between axes of tensors of stresses and strain rates change jump-wise. The discrete medium shows the properties of the continuum model of granular material with internal friction and dilatancy. The authors discuss a criterion of the continuum model to be equivalent to the initial discrete model. Applicability of the numerical results to the continuum modeling of deformation is demonstrated.