A. Munjiza

A combined finite‐discrete element method in transient dynamics of fracturing solids

This paper discusses the issues involved in the development of combined finite/discrete element methods; both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems. The finite element representation of the solid region is combined with progressive fracturing, which leads to the formation of discrete elements, which may be composed of one or more deformable finite elements. The applicability of the approach is demonstrated by the solution of a range of examples relevant to various industrial sections.

NBS contact detection algorithm for bodies of similar size

Large-scale discrete element simulations, as well as a whole range of related problems, involve contact of a large number of separate bodies. In this context an efficient and robust contact detection algorithm is necessary. There has been a number of contact detection algorithms with total detection time (CPU time needed to detect all couples close to each other) proportional to Nln(N) (where N is the total number of separate bodies) reported in recent years. In this work a contact detection algorithm with total detection time proportional to N is reported. The algorithm is termed NBS, which stands for no binary search. In other words, the proposed algorithm involves no binary search at any stage. In addition the performance of the algorithm in terms of total detection time is not influenced by packing density, while memory requirements are insignificant. The only limitation of the algorithm is its applicability to the systems comprising bodies of similar size.

Penalty function method for combined finite–discrete element systems comprising large number of separate bodies

Large-scale discrete element simulations, the combined finite–discrete element method, DDA as well as a whole range of related methods, involve contact of a large number of separate bodies. In the context of the combined finite–discrete element method, each of these bodies is represented by a single discrete element which is then discretized into finite elements. The combined finite–discrete element method thus also involves algorithms dealing with fracture and fragmentation of individual discrete elements which result in ever changing topology and size of the problem. All these require complex algorithmic procedures and significant computational resources, especially in terms of CPU time. In this context, it is also necessary to have an efficient and robust algorithm for handling mechanical contact. In this work, a contact algorithm based on the penalty function method and incorporating contact kinematics preserving energy balance, is proposed and implemented into the combined finite element code. Copyright

A novel iterative direct-forcing immersed boundary method and its finite volume applications

We present a novel iterative immersed boundary (IB) method in which the body force updating is incorporated into the pressure iterations. Because the body force and pressure are solved simultaneously, the boundary condition on the immersed boundary can be fully verified. The computational costs of this iterative IB method is comparable to those of conventional IB methods. We also introduce an improved body force distribution function which transfers the body force in the discrete volume of IB points to surrounding Cartesian grids totally. To alleviate the demanding computational requirements of a full-resolved direct numerical simulation, a wall-layer model is presented. The accuracy and capability of the present method is verified by a variety of two- and three-dimensional numerical simulations, ranging from laminar flow past a cylinder and a sphere to turbulent flow around a cylinder. The improvement of the iterative IB method is fully demonstrated and the influences of different body force distribution strategies is discussed.

Y-GUI : A graphical user interface and pre-processor for the combined finite-discrete element code, Y2D, incorporating material heterogeneity

Numerical modelling of a discontinuous medium has gained much popularity in recent decades. The combined finite-discrete element method (FEM/DEM) is a state-of-the-art numerical modelling technique pioneered in the mid-1990s. Y2D is a robust two-dimensional FEM/DEM research code developed by Munjiza in 2004. The major limitations of this code are (1) the lack of a graphical user interface (GUI) meaning that all pre-processing has to be made directly on an ASCII input file and (2) the inability of dealing with heterogeneous media. This contribution presents the first GUI and pre-processor, known as Y-GUI, developed for Y2D and the implementation of a new algorithm that allows for the use of heterogeneous materials. In the text all major FEM/DEM concepts are described, together with the main features available in the Y-GUI. The use of Y-GUI is presented in detail and some of its functionalities, including the heterogeneity module to be used to randomly assign materials to a mesh, are introduced. At the end of the manuscript, four case studies, including Brazilian tests of a homogeneous and a layered rock sample and a rock avalanche, are presented.

On the prediction of void porosity and packing of rock particulates

The objective of this paper is to provide a discursive platform for the broad spectrum of practitioners and researchers concerned with packing characteristics of rock particulates. The paper focuses on void porosity prediction in gravity-dominated packing, drawing on the breadth of disciplines that have addressed this problem. The different approaches to accommodating size distribution, shape, looseness of assembly and absolute size are variously explained or touched upon. The main part of the paper is a selective summary of recent contributions to semianalytical and empirical prediction models. An attempt to compare several porosity prediction models for a range of uniformity in the size distribution is reported. The reasons for differences are discussed. This leads to a consideration of the vital role that numerical modelling of particulate behaviour can play and a number of recent research developments in particle pack simulation are highlighted. The main problems associated with the numerical modelling of rock particulates are found to be those related to the modelling of the interaction between angular irregular particles with real shapes. 3D visualisation results are illustrated from a space filling tetrahedron assembly model and a dynamic interaction model for real-shaped particles under development by the authors. The paper concludes that better approaches for characterising the shapes of populations of rock particulates will be required to service the numerical models of the future.

Direct numerical simulation of sediment entrainment in turbulent channel flow

In this paper, the entrainment and movement of coarse particles on the bed of an open channel is numerically investigated. Rather than model the sediment transport using a concentration concept, this study treats the sediment as individual particles and investigates the interaction between turbulent coherent structures and particle entrainment. The applied methodology is a combination of the direct numerical simulation of turbulent flow, the combined finite-discrete element modeling of particle motion and collision, and the immersed boundary method for the fluid-solid interaction. In this study, flow over a water-worked rough-bed consisting of 2-3 layers of densely packed spheres is adopted and the Shields function is 0.065 which is just above the entrainment threshold to give a bed-load regime. Numerical results for turbulent flow, sediment entrainment statistics, hydrodynamic forces acting on the particles, and the interaction between turbulence coherent structures and particle entrainment are presented...

Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms

Abstract In the context of the combined finite–discrete element method a number of algorithms aimed at modelling progressive failure, fracture and fragmentation of solids under extreme loading conditions have been proposed in the last few years. The fracture patterns obtained by recently proposed algorithms are impressive. However, sensitivity of these algorithms to both mesh size and mesh orientation remains an open question. The aim of this paper is to further investigate sensitivity to mesh size of the recently proposed so called combined single and smeared crack model. Sensitivity to mesh orientation is outside scope of this paper and is discussed only qualitatively.

Large scale simulation of red blood cell aggregation in shear flows

Aggregation of highly deformable red blood cells (RBCs) significantly affects the blood flow in the human circulatory system. To investigate the effect of deformation and aggregation of RBCs in blood flow, a mathematical model has been established by coupling the interaction between the fluid and the deformable solids. The model includes a three-dimensional finite volume method solver for incompressible viscous flows, the combined finite-discrete element method for computing the deformation of the RBCs, a JKR model-Johnson, Kendall and Roberts (1964-1971) (Johnson et al., 1971) to take account of the adhesion forces between different RBCs and an iterative direct-forcing immersed boundary method to couple the fluid-solid interactions. The flow of 49,512 RBCs at 45% concentration under the influence of aggregating forces was examined, improving the existing knowledge on simulating flow and structural characteristics of blood at a large scale: previous studies on the particular issue were restricted to simulating the flow of 13,000 aggregative ellipsoidal particles at a 10% concentration. The results are in excellent agreement with experimental studies. More specifically, both the experimental and the simulation results show uniform RBC distributions under high shear rates (60-100/s) whereas large aggregation structures were observed under a lower shear rate of 10/s. The statistical analysis of the simulation data also shows that the shear rate has significant influence on both the flow velocity profiles and the frequency distribution of the RBC orientation angles.

The combined finite–discrete element method for structural failure and collapse

Abstract A combined finite–discrete element model for failure and collapse of structural systems comprising of reinforced concrete beam or column type structural members has been developed and implemented into a combined finite–discrete element code. The results obtained using the proposed model compare well with analytical and experimental results. In addition the rotational capacities obtained are in good agreement with published experimental results.