Two-dimensional discrete element modelling of bender element tests on an idealised granular material

The small-strain (elastic) shear stiffness of soil is an important parameter in geotechnics. It is required as an input parameter to predict deformations and to carry out site response analysis to predict levels of shaking during earthquakes. Bender element testing is often used in experimental soil mechanics to determine the shear (S-) wave velocity in a given soil and hence the shear stiffness. In a bender element test a small perturbation is input at a point source and the propagation of the perturbation through the system is measured at a single measurement point. The mechanics and dynamics of the system response are non-trivial, complicating interpretation of the measured signal. This paper presents the results of a series of discrete element method (DEM) simulations of bender element tests on a simple, idealised granular material. DEM simulations provide the opportunity to study the mechanics of this testing approach in detail. The DEM model is shown to be capable of capturing features of the system response that had previously been identified in continuum-type analyses of the system. The propagation of the wave through the sample can be monitored at the particle-scale in the DEM simulation. In particular, the particle velocity data indicated the migration of a central S-wave accompanied by P-waves moving along the sides of the sample. The elastic stiffness of the system was compared with the stiffness calculated using different approaches to interpreting bender element test data. An approach based upon direct decomposition of the signal using a fast-Fourier transform yielded the most accurate results.     

Micromechanics of seismic wave propagation in granular materials

In this study experimental data on a model soil in a cubical cell are compared with both discrete element (DEM) simulations and continuum analyses. The experiments and simulations used point source transmitters and receivers to evaluate the shear and compression wave velocities of the samples, from which some of the elastic moduli can be deduced. Complex responses to perturbations generated by the bender/extender piezoceramic elements in the experiments were compared to those found by the controlled movement of the particles in the DEM simulations. The generally satisfactory agreement between experimental observations and DEM simulations can be seen as a validation and support the use of DEM to investigate the influence of grain interaction on wave propagation. Frequency domain analyses that considered filtering of the higher frequency components of the inserted signal, the ratio of the input and received signals in the frequency domain and sample resonance provided useful insight into the system response. Frequency domain analysis and analytical continuum solutions for cube vibration show that the testing configuration excited some, but not all, of the system’s resonant frequencies. The particle scale data available from DEM enabled analysis of the energy dissipation during propagation of the wave. Frequency domain analysis at the particle scale revealed that the higher frequency content reduces with increasing distance from the point of excitation.     

Numerical simulation of the guided Lamb wave propagation in particle reinforced composites

This paper deals with the investigation of the Lamb wave propagation in particle reinforced composites excited by piezoelectric patch actuators. A three-dimensional finite element method (FEM) modeling approach is set up to perform parameter studies in order to better understand how the Lamb wave propagation in particle reinforced composite plates is affected by change of central frequency of excitation signal, volume fraction of particles, size of particles and stiffness to density ratio of particles. Furthermore, the influence of different arrangements is investigated. Finally, the results of simplified models using material data obtained from numerical homogenization are compared to the results of models with heterogeneous build-up. The results show that the Lamb wave propagation properties are mainly affected by the volume fraction and ratio of stiffness to density of particles, whereas the particle size does not affect the Lamb wave propagation in the considered range. As the contribution of the stiffer material increases, the group velocity and the wave length also increase while the energy transmission reduces. Simplified models based on homogenization technique enabled a tremendous drop in computational costs and show reasonable agreement in terms of group velocity and wave length.     

Propagation of solitary waves in 2D granular media: A numerical study

The impact-induced wave propagation in a model granular material composed of closely packed linearly elastic spherical particles interacting through Hertzian contact is investigated numerically using a specially adapted molecular dynamics framework. Of particular interest is the effect of the stiffness and density mismatch between main and interstitial beads on the anisotropic nature and speed of propagation of the primary compressive wave generated by a localized impact event in an extended square-packed granular medium. Two propagation regimes are observed in the numerical simulations: the first one described by a solitary wave pattern emanating from the point of impact, and the other characterized by a directional propagation of the impact energy in the principal directions of the pack. A simple model is proposed to describe the bounds between these two propagation regimes in the parametric space defined by the mass and stiffness ratios between main and interstitial particles. Maps of the normalized maximum compressive force and wave speed are presented to quantify the anisotropy of the wave propagation response.     

The influence of inter-particle friction and the intermediate stress ratio on soil response under generalised stress conditions

Previous research studies have used either physical experiments or discrete element method (DEM) simulations to explore, independently, the influence of the coefficient of inter-particle friction (μ) and the intermediate stress ratio (b) on the behaviour of granular materials. DEM simulations and experiments using photoelasticity have shown that when an anisotropic stress condition is applied to a granular material, strong force chains or columns of contacting particles transmitting relatively large forces, form parallel to the major principal stress orientation. The combined effects of friction and the intermediate stress ratio upon the resistance of these strong force chains to collapse (buckling failure) are considered here using data from an extensive set of DEM simulations including triaxial and true triaxial compression tests. For all tests both?μ and b affected the macro- and micro-scale response, however the mechanisms whereby the force chain stability was improved differ. While friction clearly enhances the inherent stability of the strong force chains, the intermediate stress ratio affects the contact density and distribution of orthogonal contacts that provide lateral support to the force chains.     

Modelling dilation in an idealised asphalt mixture using discrete element modelling

This paper investigates the use of discrete element modelling (DEM) to simulate the behaviour of a highly idealised bituminous mixture under uniaxial and triaxial compressive creep tests. The idealised mixture comprises single-sized spherical (sand-sized) particles mixed with bitumen and was chosen so that the packing characteristics are known (dense random packing) and the behaviour of the mixture will be dominated by the bitumen and complex aggregate interlock effects will be minimised. In this type of approach the effect of the bitumen is represented as shear and normal contact stiffnesses. A numerical sample preparation procedure has been developed to ensure that the final specimen is isotropic and has the correct volumetrics. Elastic contact properties have been used to investigate the effect of the shear and normal contact stiffnesses on bulk material properties. The bulk modulus was found to be linearly dependent on the normal contact stiffness and independent of the shear contact stiffness. Poisson’s ratio was found to be dependent on only the ratio of the shear contact stiffness to the normal contact stiffness. An elastic contact has been assumed for the compressive normal contact stiffness and a viscoelastic contact for shear and tensile normal contact stiffness to represent the contact behaviour in idealised mixture. The idealised mixture is found to dilate when the ratio of compressive to tensile contact stiffness increases as a function of loading time. Uniaxial and triaxial viscoelastic simulations have been performed to investigate the effect of stress ratio on the rate of dilation with shear strain for the sand asphalt. The numerical results have been validated with experimental data.     

Stress-induced anisotropy in sand under cyclic loading

The anisotropy of a granular material’s structure will influence its response to applied loads and deformations. Anisotropy can be either inherent (e.g. due to depositional process) or induced as a consequence of the applied stresses or strains. Discrete element simulations allow the interactions between individual particles to be explicitly simulated and the fabric can be quantified using a fabric tensor. The eigenvalues of this fabric tensor then give a measure of the anisotropy of the fabric. The coordination number is a particle scale scalar measure of the packing density of the material. The current study examines the evolution of the fabric of a granular material subject to cyclic loading, using two-dimensional discrete element method (DEM) simulations. Isotropic consolidation modifies and reduces the inherent anisotropy, but anisotropic consolidation can accentuate anisotropy. The ratio of the normal to shear spring stiffness at the particle contacts in the DEM model affects the evolution of anisotropy. Higher ratios reduce the degree of anisotropy induced by anisotropic consolidation. The anisotropy induced by cyclic loading depends on the amplitude of the loading cycles and the initial anisotropy.     

Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems

Piezoelectric nanobeam (PNB) offer the possibility of being used in micro-electromechanical systems and nano-electromechanical systems and the dynamic testing of such structures often produces stress wave propagation in them. This work concerns with the size-dependent wave propagation of double-piezoelectric nanobeam-systems (DPNBSs) based on Euler–Bernoulli beam model. The two piezoelectric nanobeams are coupled by an enclosing elastic medium which is simulated by Pasternak foundation. Nonlocal piezoelasticity theory is used to derive the general differential equation based on Hamilton’s principal to include those scale effects. Particular attention is paid to the wave propagation piezoelectric control of the coupled system in three cases namely in-phase wave propagation, out-of-phase wave propagation and wave propagation when one PNB is stationary. In three mentioned cases, an analytical method is proposed to obtain phase velocity; cut-off and escape frequencies of the DPNBSs. Results indicate that the imposed external voltage is an effective controlling parameter for wave propagation of the coupled system. Furthermore, the phase velocity of in-phase wave propagation is independent of elastic medium stiffness.     

Determination of the Elastic Symmetry of a Monolithic Ceramic using Bulk Acoustic Waves

A nondestructive optimal determination of elastic properties from ultrasonic bulk wave velocity measurements on a monolithic ceramic plate immersed in water is presented. This procedure, that is applicable to flat plates with unknown material properties, is based on already established methods and includes discussions, using experimental data, on the reliability of the elastic property identification, such as the stiffness tensor and the material symmetry. By solving inverse propagation problems deduced from the Christoffel equation and depending on wave speed measurements, we show that the studied sample can be described by twenty-one dependent stiffness constants and that its intrinsic elastic material symmetry was hexagonal (or transversely isotropic).     

DEM calibration of cohesive material in the ring shear test by applying a genetic algorithm framework

This research demonstrates capturing different stress states and history dependency in a cohesive bulk material by DEM simulations. An automated calibration procedure, based on the Non-dominated Sorting Genetic Algorithm, is applied. It searches for the appropriate simulation parameters of an Elasto-Plastic Adhesive contact model such that its response is best fitted to the shear stress measured in experiments. Using this calibration procedure, the optimal set of DEM input parameters are successfully found to reproduce the measured shear stresses of the cohesive coal sample in two different pre-consolidation levels. The calibrated simulation resembles the stress history dependent values of shear stress, bulk density and wall friction. Through the case study of the ring shear tester, this research demonstrates the robustness and accuracy of the calibration framework using multi-objective optimization on multi-variable calibration problems irrespective of the chosen contact model.     

Modeling progressive delamination of laminated composites by discrete element method

Discrete element method (DEM) was used to model progressive delamination of fiber reinforced composite laminates. The anisotropic composite plies were constructed through a hexagonal packing of particle elements. Contacts between the particles were represented by parallel bonds with the verified normal and shear elastic properties. The ply interface was characterized by a contact softening model with a bilinear elastic behavior which is similar to the cohesive zone model in the continuum mechanics. DCB, ELS and FRMM tests were simulated by the DEM model to assess its capability of modeling mode I, mode II and mix mode fracture of delamination, respectively. Good agreements were observed between the DEM and existing numerical and experimental results of loading curves, which confirmed that the DEM model can be used to simulate initiation and propagation of composite delamination, with more insights into microscopic material behavior, such as damage extension and plastic zone.     

Tensile stress relaxation in unsaturated granular materials

The mechanics of granular media at low liquid saturation levels remain poorly understood. Macroscopic mechanical properties are affected by microscale forces and processes, such as capillary forces, inter-particle friction, liquid flows, and particle movements. An improved understanding of these microscale mechanisms is important for a range of industrial applications and natural phenomena (e.g. landslides). This study focuses on the transient evolution of the tensile stress of unsaturated granular media under extension. Experimental results suggest that the stress state of the material evolves even after cessation of sample extension. Moreover, we observe that the packing density strongly affects the efficiency of different processes that result in tensile stress relaxation. By comparing the observed relaxation time scales with published data, we conclude that tensile stress relaxation is governed by particle rearrangement and fluid redistribution. An increased packing density inhibits particle rearrangement and only leaves fluid redistribution as the major process that governs tensile stress relaxation.     

Supercritical parametric wave phase conjugation as an instrument for narrowband analysis in ultrasonic harmonic imaging

Supercritical parametric wave phase conjugation (SWPC) is used for selection and phase conjugation of harmonic components of a nonlinear incident wave. The amplitude of the phase conjugate wave in a supercritical mode is high enough for acoustic nonlinearity of the propagation medium to appear. As a result, in particular, doubled and quadrupled frequencies of the incident wave become available for image formation at the same order of the medium nonlinearity. The improvement of the imaging system resolution because of harmonic analysis of the received acoustic signal and compensation of phase distortions caused by wave phase conjugation were observed simultaneously when the propagation medium was inhomogeneous.     

Experiments and simulations of direct shear tests: porosity, contact friction and bulk friction

The direct shear testers, in particular the Jenike cell, are widely used to measure the bulk material properties for the design of bulk handling equipment. This paper describes a study of the Jenike shear tester using both experiments and discrete element simulations. A total of 90 tests on spherical glass beads and paired glass beads were performed to study the influence of the particle shape, stress level and packing density on the bulk friction at limiting shear. The data are thus useful for validating particle scale simulations of densely packed granular systems. In an attempt to verify the predictive capability of discrete element method, closely matching 3-dimensional discrete element simulations of the shear tests were performed and compared with the experimental observations. The comparison for single spheres shows good quantitative agreement for the limiting bulk friction when there is a good match in the sample porosity. Further research is needed to produce a comprehensive validation of the discrete element method. Several salient observations from this study provide further insight into the roles of particle shape and contact friction on the resulting packing porosity and bulk friction.     

Evolution of at-rest lateral stress for cemented sands: experimental and numerical investigation

We present measurements of the evolution of the at-rest lateral stress coefficient K ₀ for cemented sands in a modified oedometer and provide additional insights into material response using discrete element method (DEM) simulations. A new scheme for the measurement of K ₀ is adapted to obtain horizontal stress for the entire stress history with parallel measurement of shear wave velocity. Results show that the horizontal stress of uncemented sand linearly increases, while debonding in cemented sands is characterized by a non-linear evolution of horizontal stress. Cement content governs the stress regime in which decementation initiates. The at-rest lateral stress coefficient of cemented sands increases during decementation, resulting in higher values for overconsolidated specimens. The recovery of K ₀ values is manifested at the preconsolidation stress during reloading. Cemented sands collapse followed by decementation and subsequent changes in K ₀ values. The DEM simulations reasonably reproduce laboratory specimen-scale response and are used to highlight the evolution of particle contact force, gradual debonding of cement, and the formation of a blocky structure in cemented sands at the particle-scale. These observations are consistent with inferred response of physical specimens at the particle scale, yet this behavior is not directly observable in the laboratory, highlighting the particular effectiveness of an integrated physical-numerical investigation. The interparticle contact stiffness of cemented sands controls the evolution of horizontal stress at low vertical stress, and the decementation causes the convergence of K ₀ values towards those of uncemented sands at high vertical stress.     

Finite element modeling of transient ultrasonic waves in linear viscoelastic media

Linear viscoelasticity offers a minimal framework within which to construct a causal model for wave propagation in absorptive media. Viscoelastic media are often described as media with `fading memory,' that is, the present state of stress is dependent on the present strain and the complete time history of strain convolved with appropriate time-dependent shear and bulk stress relaxation moduli. An axisymmetric, displacement-based finite element method for modeling pulsed ultrasonic waves in linear, homogeneous, and isotropic (LHI) viscoelastic media is developed that does not require storage of the complete time history of displacement at every node. This is accomplished by modeling stress relaxation moduli as discrete or continuous spectra of decaying exponentials and relaxation times. Details of the construction and computation of the time-dependent stiffness matrix are presented. As an application of the finite element method, a finite number of exponentials (amplitudes and relaxation times) are employed to represent a typical model for a continuous relaxation spectrum. It is demonstrated that a small number of discrete exponentials are required to model ultrasonic wave propagation of a typical band-limited pulse in a model material accurately. Previous work has shown this model to be consistent with other analytic models for wave propagation in viscoelastic media     

DEM simulations and experiments for projectile impacting two-dimensional particle packings including dissimilar material layers

The dynamic response of a two-dimensional ordered particle packing composed of nylon-66 spheres 6.35 mm in diameter impacted by a spherical projectile was investigated both experimentally and numerically using the discrete element method (DEM). First, the influence of the number of layers in the particle packing on wave propagation and post-impact movement were examined. As the number of layers increased, the contact forces reaching the base plate decreased together with the rebound velocity of the projectiles. Next, the effects of dissimilar material layers were examined. The spheres in one or two layers of the particle packing were replaced with spheres made of dissimilar materials, that is, alumina ceramic (Al₂O₃) or steel, and it was found that the scattering of the nylon spheres above the dissimilar material layers increased. The experimental results obtained using force sensors at the base plate showed that the dissimilar material layers reduced the contact forces at the base plate. Furthermore, as the mass of the dissimilar material spheres increased, the magnitude of the contact forces at the base plate decreased, and the rebound velocity of the projectile increased.     

载荷作用下EPS混凝土中弹性波传播特性研究

应用EPS混凝土来模拟含缺陷的岩石材料。对EPS粒径分别为1、2和3mm的三种EPS混凝土试样进行了载荷作用下不同频率的弹性波传播实验研究。采用单一频率脉冲叠合的方法来精确确定材料的波速,结果表明：EPS混凝土的p波波速随载荷增加在试件的开始压密实阶段有较明显的增大趋势,当试件相对密实,波速增加不是很明显;s波波速随载荷增加有一定程度增加,但幅度比p波波速增加得小得多。应用一种相对波速的方法,即将波速与当前载荷下材料的声波速度进行对比,可以较好地分析波速与载荷和频率的关系。最后对波速与载荷和频率的关系进行了理论模拟分析。此研究对于应用弹性波进行材料和结构的无损检测等技术方面有很好的参考意义。     

Real and complex Doppler effects in lossy media

The theory of the Doppler effect in the presence of lossy media and moving scatterers is investigated. Essentially two kinds of phenomena emerge, which are not distinguishable in the conventional case of lossless media. When the scatterers move uniformly, or the equation of motion involves a slowly varying velocity, it is shown that propagation in lossy media involves complex Doppler effects. The complications introduced by the received complex frequency signal are discussed. It is shown that spectrum broadening occurs, and that, in certain cases, by using judiciously chosen temporal filters, the spectral degradation of the received signal can be counteracted. The second class of phenomena is associated with periodic and harmonic motion, when the scatterer is vibrating around a fixed location. In this case the incident wave is frequency modulated by the moving scatterer, giving rise to sidebands of real frequencies.