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%.     

On sorting triangles in a delaunay tessellation

In a two-dimensional Delaunay-triangulated domain, there exists a partial ordering of the triangles (with respect to a vertex) that is consistent with the two-dimensional visibility of the triangles from that vertex. An equivalent statement is that a polygon that is star-shaped with respect to a given vertex can be extended, one triangle at a time, until it includes the entire domain. Arbitrary planar triangulations do not possess this useful property which allows incremental processing of the triangles.This work was partially supported by the National Science Foundation's US-Italy Collaborative Research Program under Grant INT-8714578 and Information, Robotics, and Intelligent Research Grant IRI-8704781.     

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.     

Low temperature synthesis of aluminium titanate by an aqueous sol-gel route

Formation of aluminium titanate (AT) has been achieved at low temperature through sol-gel process using boehmite and titanium hydroxide as precursors by controlling the particle size at nanoscale followed by in-situ peptisation. The formations of AT phase, particle size distributions, sintering and thermal expansion characteristics, and microstructural features have been reported. DTA and XRD analysis have been performed to confirm the formation of AT. A 94% relative density was obtained for aluminium titanate sintered at 1550 °C with controlled grain size in the range of 2-3 μm.     

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.     

ON THE MODELLING OF PARTICLE-BODY INTERACTIONS IN STOKES FLOWS INVOLVING A SPHERE AND CIRCULAR DISC OR A TORUS AND CIRCULAR CYLINDER USING POINT SINGULARITIES

Few exact solutions of the Stokes equations are known, even for steady or quasi-steady flows, involving finite sized bodies, and numerical techniques generally have to be resorted to for finding solutions. However, quite effective modelling of flows involving complicated boundary geometries is possible using the three-dimensional Stokeslet and rotlet point singularities. Two problems are studied in detail. In the first example, exact solutions for the three-dimensional Stokeslet and rotlet placed axisymmetrically along the axis of a circular disc are found and combined with Brenner's first order interaction formulae to determine the effect of the presence of the disc on the force and torque acting on a particle whose dimensions are small compared with its distance from the disc. The results are compared with those of a full numerical integration of the Stokes equations for a sphere translating towards a disc. In the second example, Brenner's first order wall correction theory is applied to the motion of a particle in a circular cylinder using the exact solutions for a torus translating or rotating in isolation. The theoretical predictions for the drag on a torus settling symmetrically in a circular cylinder are compared with those determined experimentally.