A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load-displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.     

Sphere packing with a geometric based compression algorithm

An efficient algorithm for the random packing of spheres can significantly save the cost of the preparation of an initial configuration often required in discrete element simulations. It is not trivial to generate such random packing at a large scale, particularly when spheres of various sizes and geometric domains of different shapes are present. Motivated by the idea of compression complemented by an efficient physical process to increase packing density, shaking, a new approach, termed compression algorithm, is proposed in this work to randomly fill any arbitrary polyhedral or cylindrical domains with spheres of various sizes. The algorithm features both simplicity and high efficiency. Tests show that it takes 181 s on a 1.4-GHz PC to complete the filling of a cylindrical domain with a total number of 26,787 spheres, achieving a packing density of 52.89%.     

Effect of vibration condition and inter-particle frictions on the packing of uniform spheres

We present a numerical study of the packing of uniform spheres under three-dimensional vibration using the discrete element method (DEM), focusing on the effects of vibration condition (amplitude and frequency) and inter-particle frictions (sliding and rolling frictions). The results are analysed in terms of packing density, coordination number (CN), radial distribution function (RDF) and pore structure. It is shown that increasing either the vibration amplitude or frequency causes packing density to increase initially to a maximum and then decrease. Both vibration frequency and amplitude should be considered to characterize the effect of vibration process on packing structure. The sliding and rolling frictions between particles can decrease packing density since they dissipate energy, although the effect of rolling friction is less significant. In line with the change of packing density, microstructural properties such as CN, RDF and pore distribution also change: a looser packing often corresponds to smaller CN, less peaked RDF and larger but more widely distributed pores.     

Applications of the discrete element method in mechanical engineering

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples. Commemorative Contribution.     

A generalized approach to the reconstruction of a restricted class of digitized planar curves

Reconstruction of an original continuous curve and the estimation of its parameters from the digitized version of the curve is a challenging problem, as quantization always causes some loss of information. In this paper, we have developed a scheme for reconstruction which is applicable to a class of curves having at the most two parameters. The class of curves for which the scheme works has also been characterized. We have shown that for one-parameter curves the exact domain of values of the parameter can be obtained. But in the two-parameter case, only the smallest rectangle containing the domain can be realised. The distinctive feature of our scheme is that it provides a unified approach to solve the reconstruction and the domain-finding problem for a class of curves.     

Scanning electron microscope electron detector with a radial type discrete dynode electron multiplier

A discrete dynode electron multiplier with radial flux of electrons was built and tested in the range of low‐voltage scanning electron microscopy as a backscattered electron detector of topographic contrast. The multiplier collects backscattered electron emitted in a specific range of take‐off angles and over the whole azimuth angular range enabling large solid collection angle. Multipliers with different dynode shapes were studied theoretically with the use of the software for particle optics and three assemblies were built and tested experimentally. The gain estimation, assessment of the type of detected electrons (secondary electron or backscattered electron), imaging the spatial collection efficiency and signal‐to‐noise measurements were performed.     

Use of a neural network to link AFM etch patterns to plasma parameters

Plasmas play a critical role in depositing thin films or etching fine patterns while manufacturing integrated circuits. A new model for plasma diagnosis is presented. This was accomplished by linking atomic force microscopy (AFM) to plasma parameters using a neural network. Experimental AFM data were collected during the etching of silicon oxynitride films in C₂F₆ inductively coupled plasma. Surface roughness of etched patterns was characterized by means of discrete wavelet transformation. This led to the construction of three vertical (type I), diagonal (type II), and horizontal (type III) wavelet coefficient-based models. The performance of diagnosis models was evaluated in terms of the prediction and recognition accuracies. Both accuracies were optimized as a function of the number of hidden neurons. Comparisons revealed that the type I model yielded the largest recognition and the smallest prediction error. This was demonstrated even under stricter monitoring conditions. More improved diagnosis is expected by enhancing AFM resolution.     

Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle material

In this work we present the discrete models for dynamic fracture of structures built of brittle materials. The models construction is based on Voronoi cell representation of the heterogeneous structure, with the beam lattice network used to model the cohesive and compressive forces between the neighboring cells. Each lattice component is a geometrically exact shear deformable beam which can describe large rigid body motion and the most salient fracture mechanisms. The latter can be represented through the corresponding form of the beam constitutive equations, which are derived either at microscale with random distribution of material properties or at a mesoscale with average deterministic values. The proposed models are also placed within the framework of dynamics, where special attention is paid to constructing the lattice network mass matrix as well as the corresponding time-stepping schemes. Numerical simulations of compression and bending tests is given to illustrate the models performance.     

Convolutional solutions of partial difference equations

A significant part of the theory of one-dimensional linear shift-invariant systems is based on the concept of weighting function (or impulse response): the output is the convolution of the weighting function with the input. This paper introduces the concept of linear translation-invariant systems and uses this notion in studying impulse response, z-transforms, and transfer functions for multidimensional systems.     

Wake and aerodynamics loads in multiple bodies—application to turbomachinery blade rows

Two-dimensional, unsteady flow around bodies of complex geometry (or multiple bodies) at high Reynolds number is simulated using the vortex method. This method is modified to take into account the sub-grid scale phenomena through a second order velocity structure function model adapted to the Lagrangian scheme. The dynamics of the body wake is computed using the convection-diffusion splitting algorithm; the convection process is carried out with a Lagrangian Adams-Bashforth time-marching scheme and the diffusion process is simulated using the random walk method. The pressure distribution is obtained using an integral equation derived from the pressure Poisson equation, which was first developed for a single body. Results for the numerical simulation around a linear cascade of airfoils are presented. As the flow is periodic in the y direction, the discrete vortex shedding need only be considered for a reference airfoil. The flow characteristics around the NACA 65-410 series airfoils are calculated and comparisons are made with results available in the literature.