Y.T. Feng

Discrete thermal element modelling of heat conduction in particle systems: Basic formulations

This paper proposes a novel numerical methodology, termed the discrete thermal element method (DTEM), for the effective modelling of heat conduction in systems comprising a large number of circular particles in 2D cases. Based on an existing analytical integral solution for the temperature distribution over a circular domain subjected to the Neumann boundary condition, a linear algebraic system of thermal conductivity equations for each particle is derived in terms of the average temperatures and the resultant fluxes at the contact zones with its neighboring particles. Thus, each particle is treated as an individual element with the number of (temperature) unknowns equal to the number of particles that it is in contact with. The element thermal conductivity matrix can be very effectively evaluated and is entirely dependent on the characteristics of the contact zones, including the contact positions and contact angles. This new element shares the same form and properties with its conventional thermal finite element counterpart. In particular, the whole solution procedure can follow exactly the same steps as those involved in the finite element analysis. Unlike finite elements or other modern numerical techniques, however, no discretization errors are involved in the discrete thermal elements. The modelling error mainly stems from the assumption made about the heat flux distribution within the contact zones. Based on some theoretical work, an enhanced version is suggested to improve the approximation. The numerical assessment against finite element results indicates that the basic version of DTEM can achieve a very reasonable solution accuracy, while the enhanced version further improves the accuracy to a high level. In addition, thermal resistance phenomena between the contact zones can be readily incorporated into the current modelling framework.

A new criterion for determination of initial loading parameter in arc-length methods

The arc-length method has been extensively applied in the last decade to trace solution paths in nonlinear static structural problems. The sign of the loading parameter increment in the predictor phase of the method, however, must be determined according to some criteria which are not well established. By further investigation of the approach within the framework of continuation methods in this paper, a new criterion has been proposed, which can be incorporated into both direct and iterative solvers, and has proved to be very successful for the test problems considered.

Parallelised finite/discrete element simulation of multi‐fracturing solids and discrete systems

This paper outlines a dynamic domain decomposition‐based parallel strategy for combined finite/discrete element analysis of multi‐fracturing solids and discrete systems. Attention is focused on the parallelised interaction detection between discrete objects. Two graph representation models for discrete objects in contact are proposed which lay the foundation of the current development. In addition, a load imbalance detection and re‐balancing scheme is also suggested to enhance the parallel performance. Finally, numerical examples are provided to illustrate the parallel performance achieved with the current implementation.

A 2D polygon/polygon contact model: algorithmic aspects

This paper proposes an energy‐based general polygon to polygon normal contact model in which the normal and tangential directions, magnitude and reference contact position of the normal contact force are uniquely defined. The model in its final form is simple and elegant with a clear geometric perspective, and also possesses some advanced features. Furthermore, it can be extended to a more complex situations and in particular, it may also provide a sound theoretical foundation to possibly unifying existing contact models for all types of (convex) objects.

CONJUGATE GRADIENT METHODS FOR SOLVING THE SMALLEST EIGENPAIR OF LARGE SYMMETRIC EIGENVALUE PROBLEMS

SUMMARY In this paper, a detailed description of CG for evaluating eigenvalue problems by minimizing the Rayleigh quotient is presented from both theoretical and computational viewpoints. Three variants of CG together with their asymptotic behaviours and restarted schemes are discussed. In addition, it is shown that with a generally selected preconditioning matrix the actual performance of the PCG scheme may not be superior to an accelerated inverse power method. Finally, some test problems in the finite element simulation of 2-D and 3-D large scale structural models with up to 20200 unknowns are performed to examine and demonstrate the performances.

A discrete particle model and numerical modeling of the failure modes of granular materials

Purpose – To present a discrete particle model for granular materials.Design/methodology/approach – Starting with kinematical analysis of relative movements of two typical circular grains with different radii in contact, both the relative rolling and the relative sliding motion measurements at contact, including translational and angular velocities (displacements) are defined. Both the rolling and sliding friction tangential forces, and the rolling friction resistance moment, which are constitutively related to corresponding relative motion measurements defined, are formulated and integrated into the framework of dynamic model of the discrete element method.Findings – Numerical results demonstrate that the importance of rolling friction resistance, including both rolling friction tangential force and rolling friction resistance moment, in correct simulations of physical behavior in particulate systems; and the capability of the proposed model in simulating the different types of failure modes, such as the...

Performance comparisons of tree‐based and cell‐based contact detection algorithms

Purpose – The main purpose of this paper is to compare the performance of three commonly used global search algorithms, namely tree‐based augmented spatial digital tree, cell‐based no binary search and D‐cell, in the discrete element simulations.Design/methodology/approach – A large number of test cases with up to five million particles/discrete objects are employed to numerically examine the computational costs of the three search algorithms and their performance is compared.Findings – Comprehensive comparisons reveal that the D‐cell is more efficient than the tree‐based search algorithms for large‐scale problems. The parametric study of the D‐cell algorithm itself shows that the performance of the algorithm is strongly dependent on the cell dimension chosen.Research limitations/implications – The only limitation of the current work is that the tested domain shape is regular, and thus more complex domain shapes may need to be considered.Originality/value – The paper provides clear guidance regarding the ...

A time-adaptive space-time finite element method for incompressible Lagrangian flows with free surfaces: computational issues

Abstract In order to further enhance the performance of the space-time Galerkin/least-squares method for solving incompressible Navier–Stokes problems involving free surfaces, issues related to the solution strategy and time adaptivity are addressed . Due to the a priori unknown boundary positions, a nonlinear system of equations normally arises at each space-time slab, which is solved by the Newton–Raphson approach . In addition, a linear system of equations for velocity and pressure that provides an alternative approach to the solution of the problem is also derived in this paper. This linear solution scheme can significantly reduce the computational costs in terms of computer CPU time and memory requirements without the sacrifice of the solution accuracy if the time-step size is sufficiently small. Furthermore, the possibility of adaptively adjusting time-step size is fully exploited. By choosing the volume loss rate as an error indicator, a simple adaptive time-stepping scheme is presented. Finally several numerical examples are provided to assess the performances of the proposed schemes.

A block conjugate gradient method applied to linear systems with multiple right-hand sides

Abstract With the generalization of the Conjugate Gradient (CG) method, a Block CG (BCG) is presented in this paper, which can simultaneously solve symmetric and positive definite linear systems with multiple right-hand sides and still preserves all the properties of the standard CG method. Several techniques related to the efficiency enhancement of BCG, including initial residual vectors orthogonalization and flexible convergence control, are also proposed. Finally, the performances of BCG are investigated on three numerical examples. In these cases improvements between 30% and 200% in terms of both CPU time and iteration requirements are achieved by the BCG method in comparison with the standard CG approach.

On upscaling of discrete element models: similarity principles

Purpose – The main purpose of this paper is to derive a set of similarity principles for discrete element modelling so that a numerical model can exactly reproduce the physical phenomenon concerned. Design/methodology/approach – The objective is achieved by introducing the concepts of particle “strain” and “stress” so that some equivalence between the physical system and the numerical model can be established. Findings – Three similarity principles, namely geometric, mechanical and dynamic, under which the numerical model can exactly reproduce the mechanical behaviour of a physical model are proposed. In particular, the concept of the scale invariant interaction law is further introduced. The scalability of a number of most commonly used interaction laws in the discrete element modelling is examined. Research limitations/implications – This is a preliminary research for a very important and challenging topic. More research, particularly in the understanding of the convergent properties of discrete element models, is needed. Originality/value – The paper provides some important theoretical guidances to computational modelling of particle systems using discrete element techniques.