Influence of particle shape on the shear behavior of superellipsoids by discrete element method in 3D

This paper aims to study the influence of particle shape on the shear strength of superellipsoidal particles by Discrete Element Method (DEM) simulations of triaxial tests in 3D. A total of forty-nine types of equiaxed superellipsoidal particles from three evolution paths have been created. The definition of effective porosity has been proposed. Our findings show that both the particle sphericity and roundness affect the shear strength of the superellipsoidal particle system. Under the mutual impact of initial porosity and particle shape, the simulation results of shear strength and volumetric strains present a trend of initially decreasing and subsequently increasing. The microstructure evolution of superellipsoidal particles during the shearing process is observed microscopically. The anisotropy of fabric reveals the mechanism of effective porosity and sphericity influencing the macroscopic shear strength at the particle scale.     

Linear-frictional contact model for 3D discrete element simulations of granular systems

The linear-frictional contact model is the most commonly used contact mechanism for discrete element (DEM) simulations of granular materials. Linear springs with a frictional slider are used for modeling interactions in directions normal and tangential to the contact surface. Although the model is simple in two dimensions, its implementation in 3D faces certain subtle challenges, and the particle interactions that occur within a single time step require careful modeling with a robust algorithm. The paper details a three-dimensional algorithm that accounts for the changing direction of the tangential force within a time step, the transition from elastic to slip behavior within a time step, possible contact sliding during only part of a time step, and twirling and rotation of the tangential force during a time step. Without three of these adjustments, errors are introduced in the incremental stiffness of an assembly. Without the fourth adjustment, the resulting stress tensor is not only incorrect but it is also no longer a tensor. The algorithm also computes the work increments during a time step, both elastic and dissipative.     

Finite element modeling of lamb wave propagation in anisotropic hybrid materials

A finite element approach for modeling of acoustic emission sources and signal propagation in hybrid multi-layered plates is presented. Modeling results are validated by Laser vibrometer measurements and comparison to calculated dispersion curves. We investigate hybrid plates as typically found in composite pressure vessels, composed of fiber reinforced polymers with arbitrary stacking sequences and attached metal or polymer materials. Hybrid plate thickness, the ratio between anisotropic and isotropic materials and material properties are varied. Lamb-wave propagation in a geometry representative of a pressure vessel is modeled. It is demonstrated, that acoustic emission sources in multi-layered structures can cause Lamb-waves superimposed by guided waves within the individual layers.     

The importance of modelling ballast particle shape in the discrete element method

The discrete element method has been used to model railway ballast. Particles have been modelled using both spheres and clumps of spheres. A simple procedure has been developed to generate clumps which resemble real ballast particles much more so than spheres. The influence of clump shape on the heterogeneous stresses within an aggregate has been investigated, and it has been found that more angular clumps lead to a greater degree of homogeneity. A box test consisting of one cycle of sleeper load after compaction has been performed on an aggregate of spheres and also on an alternative aggregate of clumps. The interlocking provided by the clumps provides a much more realistic load- deformation response than the spheres and the clumps will be the basis for future work on ballast degradation under cyclic loading.     

Application of 3D time domain boundary element formulation to wave propagation in poroelastic solids

The dynamic responses of fluid-saturated semi-infinite porous continua to transient excitations such as seismic waves or ground vibrations are important in the design of soil-structure systems. Biot's theory of porous media governs the wave propagation in a porous elastic solid infiltrated with fluid. The significant difference to an elastic solid is the appearance of the so-called slow compressional wave. The most powerful methodology to tackle wave propagation in a semi-infinite homogeneous poroelastic domain is the boundary element method (BEM). To model the dynamic behavior of a poroelastic material in the time domain, the time domain fundamental solution is needed. Such solution however does not exist in closed form. The recently developed ‘convolution quadrature method’, proposed by Lubich, utilizes the existing Laplace transformed fundamental solution and makes it possible to work in the time domain. Hence, applying this quadrature formula to the time dependent boundary integral equation, a time-stepping procedure is obtained based only on the Laplace domain fundamental solution and a linear multistep method. Finally, two examples show both the accuracy of the proposed time-stepping procedure and the appearance of the slow compressional wave, additionally to the other waves known from elastodynamics.     

Simulation of crack propagation in anisotropic structures using the boundary element shape sensitivities and optimisation techniques

Using the boundary element shape sensitivities of multi-region domains coupled with an optimisation algorithm and an automatic mesh generator, the crack kink angle and propagation path in anisotropic elastic solids are predicted. The maximum strain energy release rate criterion, best suited for the composite structures, has been employed. In contrast to the J-integral method, which would require the computation of stresses and strains at a series of internal points, here by direct differentiation of the structural response the strain energy release rates at the existing crack tip and new cracks for the period of crack growth are determined. The length of each kinked crack is treated as the shape design variable. The shape variable is then associated with the coordinates of a series of boundary nodes located on the new crack surface. Thus, the relevant velocity terms are applied together in the sensitivity analysis with respect to that variable to determine the energy release rate, which is the derivative of the total strain energy with respect to the crack length extension. Wherever possible the results are compared with the existing experimental, analytical and/or numerical results reported in the literature, in which good agreement is observed. It is shown that the present method is computationally more accurate and efficient. Two example problems with different anisotropic material properties are presented to validate the applications of this formulation. The results show that material anisotropy has a profound influence on the crack propagation of composites.     

Effect of stress wave shape on the crack propagation velocity in cyclic delayed failure

Crack propagation velocity in delayed failure under superposed repeating load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{R}}$, was compared with that under static load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$Two peaks appear on the relation between decreasing rate of crack propagation velocity, $\text{1-β = 1 ? (}\text{d}\text{a/}\text{d}\text{t))}{}_{\mathrm{R}}\text{/(}\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$ and frequency, ?, both under sinusoidal and square load. By changing the ratio of holding time at maximum stress intensity factor to that at minimum stress intensity factor in square load, it was deduced that the existence of two peaks on the 1 ? β vs $\text{f}$ curve was caused by an asymmetric interaction between hydrogen atoms and cyclic moving of the position with triaxial tensile stress at crack tip. Moreover, the relation between 1 ? β and $\text{f}$ under the positive or negative saw tooth load could be well explained by the interaction model.     

Finite element simulations of poly-crystalline shape memory alloys based on a micromechanical model

We present a finite element implementation of a micromechanically motivated model for poly-crystalline shape memory alloys, based on energy minimization principles. The implementation allows simulation of anisotropic material behavior as well as the pseudo-elastic and pseudo-plastic material response of whole samples. The evolving phase distribution over the entire specimen is calculated. The finite element model predicts the material properties for a relatively small number of grains. For different points of interest in the specimen the model can be consistently evaluated with a significantly higher number of grains in a post-processing step, which allows to predict the re-orientation of martensite at different loads. The influence of pre-texture on the material’s properties, due to some previous treatment like rolling, is discussed.     

3D dynamics of discrete element systems comprising irregular discrete elements—integration solution for finite rotations in 3D

An algorithm for transient dynamics of discrete element systems comprising a large number of irregular discrete elements in 3D is presented. The algorithm is a natural extension of contact detection, contact interaction and transient dynamics algorithms developed in recent years in the context of discrete element methods and also the combined finite‐discrete element method. It complements the existing algorithmic procedures enabling transient motion including finite rotations of irregular discrete elements in 3D space to be accurately integrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of a triangulation based approach for specimen generation for discrete element simulations

Discrete element methods are emerging as useful numerical analysis tools for engineers concerned with granular materials such as soil, food grains, or pharmaceutical powders. Obviously, the first step in a discrete element simulation is the generation of the geometry of the system of interest. The system geometry is defined by the boundary conditions as well as the shape characteristics (including size) and initial coordinates of the particles in the system. While a variety of specimen generation methods for particulate materials have been developed, there is no uniform agreement on the optimum specimen generation approach. This paper proposes a new triangulation based approach that can easily be implemented in two or three dimensions. The concept of this approach (in two dimensions) is to triangulate a system of points within the domain of interest, creating a mesh of triangles. Then the particles are inserted as the incircles of these triangles. Extension to three dimensions using a mesh of tetrahedra and inserting the inspheres is relatively trivial. The major advantages of this approach include the relative simplicity of the algorithm and the small computational cost associated with the preparation of an initial particle assembly. The sensitivity of the characteristics of the particulate material that is generated to the topology of the triangular mesh used is explored. The approach is compared with other currently used methods in both two and three dimensions. These comparisons indicate that while this approach can successfully generate relatively dense two-dimensional particle assemblies, the three- dimensional implementation is less effective at generating dense systems than other available approaches. The research presented in this paper made use of software developed by other researchers. For the two-dimensional study the program Triangle developed by Jonathan Shewchuk was used. The three-dimensional analysis used the Geompack++ program developed by Barry Joe as well as an implementation of the Jodrey and Tory (1985) algorithm by Monika Bargiel and Jacek Moscinski called NSCP3D.     

Neumann exterior wave propagation problems: computational aspects of 3D energetic Galerkin BEM

In this work, we consider as model problem an exterior 3D wave propagation Neumann problem reformulated in terms of a space–time hypersingular boundary integral equation with retarded potentials. This latter is set in the so-called energetic weak form, recently proposed in Aimi et al. (Int J Numer Methods Eng 80:1196–1240, 2009; CMES 58:185–219, 2010), regularized as in Frangi (Int J Numer Methods Eng 45:721–740, 1999) and then approximated by the Galerkin boundary element method. Details on the discretization phase and, in particular, on the computation of integrals, double in time and double in space, constituting the elements of the final linear system matrix are given and analyzed. Various numerical results and simulations are presented and discussed.     

Numerical calculations of elastic wave propagation in anisotropic thin films deposited on substrates

In this work, we present a generalized numerical model to study the dispersion curves of elastic waves in anisotropic thin layer/substrate systems. Dispersion curves as a function of wave frequency for different propagation angles are calculated. The nature of the mode (Rayleigh or Love) is identified by analyzing the polarization of the three-dimensional displacement field. This numerical model has been applied to the system Au(0 0 1)/Ni(0 0 1).     

Simulation of three-dimensional elastoacoustic wave propagation based on a Discontinuous Galerkin spectral element method

In this article, we present a numerical discretization of the coupled elastoacoustic wave propagation problem based on a discontinuous Galerkin spectral element approach in a three-dimensional setting. The unknowns of the coupled problem are the displacement field and the velocity potential, in the elastic and the acoustic domains, respectively, thereby resulting in a symmetric formulation. After stating the main theoretical results, we assess the performance of the method by convergence tests carried out on both matching and nonmatching grids, and we simulate realistic scenarios where elastoacoustic coupling occurs. In particular, we consider the case of Scholte waves, the scattering of elastic waves by an underground acoustic cavity, and a problem of marine seismic exploration. Numerical simulations are carried out by means of the code SPEED , available at http://speed.mox.polimi.it .     

Recent progress on the discrete element method simulations for powder transport systems: A review

Powder transport systems are ubiquitous in various industries, where they can encounter single powder flow, two-phase flow with solids carried by gas or liquid, and gas–solid–liquid three-phase flow. System geometry, operating conditions, and particle properties have significant impacts on the flow behavior, making it difficult to achieve good transportation of granular materials. Compared to experimental trials and theoretical studies, the numerical approach provides unparalleled advantages over the investigation and prediction of detailed flow behavior, of which the discrete element method (DEM) can precisely capture complex particle-scale information and attract a plethora of research interests. This is the first study to review recent progress in the DEM and coupled DEM with computational fluid dynamics for extensive powder transport systems, including single-particle, gas–solid/solid–liquid, and gas–solid–liquid flows. Some important aspects (i.e., powder electrification during pneumatic conveying, pipe bend erosion, non-spherical particle transport) that have not been well summarized previously are given special attention, as is the application in some new-rising fields (ocean mining, hydraulic fracturing, and gas/oil production). Studies involving important large-scale computation methods, such as the coarse grained DEM, graphical processing unit-based technique, and periodic boundary condition, are also introduced to provide insight for industrial application. This review study conducts a comprehensive survey of the DEM studies in powder transport systems.     

3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions

In this paper, the traction boundary element method (TBEM) and the boundary element method (BEM), formulated in the frequency domain, are combined so as to evaluate the 3D scattered wave field generated by 2D fluid-filled thin inclusions. This model overcomes the thin-body difficulty posed when the classical BEM is applied. The inclusion may exhibit arbitrary geometry and orientation, and may have null thickness. The singular and hypersingular integrals that appear during the model's implementation are computed analytically, which overcomes one of the drawbacks of this formulation. Different source types such as plane, cylindrical and spherical sources, may excite the medium. The results provided by the proposed model are verified against responses provided by analytical models derived for a cylindrical circular fluid-filled borehole.The performance of the proposed model is illustrated by solving the cases of a flat fluid-filled fracture with small thickness and a fluid-filled S-shaped inclusion, modelled with both small and null thickness, all of which are buried in an unbounded elastic medium. Time and frequency responses are presented when spherical pulses with a Ricker wavelet time evolution strikes the cracked medium. To avoid the aliasing phenomena in the time domain, complex frequencies are used. The effect of these complex frequencies is removed by rescaling the time responses obtained by first applying an inverse Fourier transformation to the frequency domain computations. The numerical results are analysed and a selection of snapshots from different computer animations is given. This makes it possible to understand the time evolution of the wave propagation around and through the fluid-filled inclusion.     

Effect of paddle rotational speed on particle mixing behavior in electrophotographic system by using parallel discrete element method

The objective of this paper is to investigate the effect of paddle rotational speed on the mixing behavior in an agitation process of an electrophotographic system by using parallel DEM. The mixing behaviors of beads with different sizes and densities were measured at various paddle rotational speeds by using a high-speed video camera, and were compared with the simulation results. A good agreement in the mixing behavior was obtained and the changes in particle velocity during the mixing were comparable. The simulation for mixing behavior of larger carrier particles suggested that the radial particle mixing was much faster than the axial one. The faster radial mixing is attributed to the fact that there are two radial flows in the system; the one is over the shaft, the other is between the paddle and shaft. The extent of mixing depended on the number of paddle rotations when the rotational speed is larger than 100 rpm, while the mixing under 50 rpm is completed at a smaller number of rotations.     

Impact identification on a sandwich plate from wave propagation responses

This study investigates the use of an impact detection algorithm to locate a potentially damaging impact on an orthotropic plate by detecting the stress waves generated by such an event. The proposed algorithm was tested experimentally on a sandwich plate by using ultrasonic signals. The arrival times of stress waves at different frequencies at the sensor locations were determined by analyzing the recorded signals using the wavelet transforms. The stress wave propagation phenomenon was characterized by measuring the propagation speeds along different directions. This data along with the sensor co-ordinates were input into the impact detection algorithm, which uses the difference in time of flight to the sensors and trigonometric identities to locate impact source locations. The accuracy of the method was demonstrated by the close agreement observed between the estimated locations for the three impact locations studied with the actual locations of the impact loads applied. In particular, maximum error in the estimation of the co-ordinates of the impact location was less than 9% for all different types of loading considered.     

Transmission line interpretation of the finite element mesh for a wave propagation problem

A one-dimensional exterior electromagnetic scattering problem is formulated using a differential equation approach followed by a finite element discretization. By interpreting the resulting linear algebraic equations as node voltage equations for a transmission line, a boundary element is obtained which satisfies the requirement of no wave reflection at the edge of the finite element region. Numerical results which show the elimination of non-physical standing waves from the scattered field are presented and discussed.     

Effect of the interrelationship of thermal and mechanical fields on the propagation of wave motions in cubically anisotropic thermoelastic materials

A characteristic equation for a system of equations of motion of a cubically anisotropic medium with allowance for the relaxation time of thermal disturbances has been obtained, and expressions for the velocities of propagation of modified elastic and thermal waves have been found. The surfaces of inverse velocities have been constructed and the influence of the effect of interrelationship of thermal and mechanical fields on the change in the phase velocities of propagation of a quasilongitudinal elastic wave and a thermal wave in different planes of a cubically anisotropic material has been analyzed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 384–388, March–April, 2008.