Engineering Computations: International Journal for Computer-Aided Engineering and Software

CUNDALL, PETER A.; HART, ROGER D.

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023851

Discrete element methods are numerical procedures for simulating the complete behaviour of systems of discrete, interacting bodies. Three important aspects of discrete element programs are examined 1 the representation of contacts 2 the representation of solid material and 3 the scheme used to detect and revise the set of contacts. A proposal is made to define what constitutes a discrete element program, and four classes of such programs are described the distinct element method, modal methods, discontinuous deformation analysis and the momentumexchange method. Several applications and examples are presented, and a list is given of suggestions for future developments.

WILLIAMS, JOHN R.; PENTLAND, ALEX P.

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023852

This paper discusses advances in interactive discrete element simulation for use in computeraided concurrent design. We highlight the computational problems of creating a virtual world populated by objects which behave much as real world objects and propose a system based on a new class of volumetric models, called superquadrics. These functions have significant advantages for calculating multibody interactions, and by coupling volumetric representation to a modal decomposition method for the physical dynamics we have been able to gain up to two orders of magnitude in efficiency. The modal method allows us to trade off high order modes for improved stability, time step magnitude, temporal aliasing and speed of response, and so provide almost real time feedback to the designer. We believe that virtual manufacturing systems will be especially useful in conceptual design, in design for manufacture and in the new thrust in concurrent design.

DOBRY, RICARDO; TANGTAT NG, AND

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023853

A general overview is presented on applications of the discrete element method DEM to granular media. A literature survey is performed of static and dynamic simulations using random arrays of compliant particles, and fortytwo references published mostly in the last ten years are identified and categorized according to a number of relevant criteria. It is concluded that the interest in the use of the technique is rapidly increasing in the research and engineering community, with applications concentrated in soil mechanics, rock mechanics, grain flow and engineering problems. Additional studies and verifications of some numerical aspects of the DEM technique are suggested including parametric studies and comparisons. Program CONBAL2 CONTACT TRUBAL in 2D developed by the authors based on TRUBAL created by Strack and Cundall, is described. CONBAL2 uses the complete Mindlin solution for the contact between two spheres and thus can be used for small strain and cyclic loading. The program is applied to study the cyclic response of uniform, medium dense to dense rounded quartz sand. Cyclic straincontrolled loading at constant volume is applied to isotropically consolidated, random arrays of 531 spheres, using cyclic strains ranging from 104 to 101. The calculated shear modulus, Gmax, constrained modulus, D, and Poisson's ratio at small strains are correlated with the confining pressure, the porosity of the array, and the coordination number. The calculated variations of secant modulus and damping ratio with cyclic strain compare favourably with the experimental results on sands compiled by Seed and Idriss. Finally, pore water pressure buildup and cyclic stiffness degradation of the material with number of cycles is calculated at a cyclic strain of 101, and the prediction is found to represent closely cyclic undrained experiments on sands. The existence of a threshold strain, yt 102, found experimentally, is also predicted by the simulations.

HOCKING, GRANT

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023854

This paper is concerned with the determination of the transient stress and deformational state of platelike discontinua subject to flexural cracking. Such a phenomenon can be easily visualized as the type of fragmentation to floating sea ice impacted by an icebreaker or offshore platform. The discrete element method is used to solve the dynamic equilibrium equations for each distinct deformable body and the interaction between bodies. Each body may deform elastically and fracture into further pieces if a brittle failure criterion for flexure is exceeded. The discrete plate element is a hybrid thinplate Kirchhoff mode lumped at element boundaries with transverse shear deformation computed at element centroids. Errors in computed stresses near point loads and cracks by the current element warrant the use of an improved mixed mode plate element. A threedimensional application of the discrete element method is presented for the case of fragmentation of floating sea ice impacting an arctic offshore platform. A semiimplicit solution scheme is introduced to overcome the stringent explicit time step stability conditions due to stiff members in the discrete element formulation.

SHI, GENHUA

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023855

A numerical model of deformable block systems that gives a unique solution for large displacement, large deformation and failure computations is presented. The forces acting on each block, from external loading or contact with other blocks, satisfy the equilibrium equations. Equilibrium is also achieved between external forces and the block stresses. Furthermore, the analysis fulfills constraints of no tension between blocks and no penetration of one block into another. Also, Coloumb's law is fulfilled at all contact positions for both static and dynamic computations. The program ready algorithms with brief derivations are stated in this paper.

IKEGAWA, Y.; HUDSON, J.A.

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023856

Until now, identification of threedimensional nonconvex concave blocks has not been accomplished. However, a direct body concept, which is introduced here, can deal with both convex and concave blocks in the same process in connection with detection of individual blocks and computation of physical quantities. Thus, the dilemma in the generalization of identifying threedimensional multiblock systems has been eliminated. The directed body concept used in geometrical identification problems makes it possible to build a novel automatic identification system for threedimensional multiblock systems. This new system eliminates the timeconsuming work on geometrical identification, and copes with a variety of applications in multibody systems, such as rock masses.

MUSTOE, GRAHAM G.W.

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023857

A generalized weighted residual method is used to formulate the discrete element method DEM for rigid or deformable bodies. It is shown that this approach provides a unified methodology for deriving many of the different discrete element techniques in current use today. This procedure is used to develop a number of different element formulations for use in problems in which the distinct bodies exhibit complex deformation behaviour such as beam or plate flexure, membrane action, and additional reinforcement of a jointed discontinuum. A covergence proof for the twodimensional beam element is given for mathematical validation. A number of examples are also presented which illustrate the usefulness of different discrete element types in engineering analyses of discontinuum problems.

TRENT, B.C.; MARGOLIN, L.G.

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023858

The distinct element method has been used to perform a number of numerical experiments, analogous to physical tests routinely carried out for real geologic materials. The ability to prescribe exactly the material properties and the boundary conditions allows us to study in detail the influence of microscopic structure on macroscopic response. These macroscopic quantities are usually the only data obtained in physical experiments. We are now in a position to formulate a general constitutive model, based on physical mechanisms and appropriate for use in a continuum code.

BATHURST, RICHARD J.; ROTHENBURG, LEO

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023859

The development of physicallycorrect models of granular behaviour under shear deformations must recognize the discrete nature of the medium and the mechanical properties of the constituent grains at the particle level. Numerical simulation of idealized granular materials offers the researcher the possibility of recovering complete information on these systems that can then guide the development of micromechanicalbased models of granular systems. A numerical technique that has proved useful in meeting this goal is the discrete element method DEM. The computer implementation of this method to observe microfeatures of idealized granular assemblies was first reported in the published literature by Cundall and Strack. Since that time a number of researchers have used the technique to explore the behaviour of idealized granular systems comprising cohesionless assemblies of discs and assemblies of discs comprising indestructible bonded contacts. The paper reviews some of the numerical simulation work that has been carried out by the authors to verify stressforcefabric relationships first proposed by Rothenburg and constitutive stressstrain laws for dense isotropic assemblies of bonded discs. The numerical technique in each case is the same and involves the solution of the equations of motion of each particle using an explicit timefinite difference algorithm which is the essential feature of the DEM.

ISSA, JAY A.; NELSON, RICHARD B.

1992 Engineering Computations: International Journal for Computer-Aided Engineering and Software

doi: 10.1108/eb023860

A numerical analysis of the micromechanical behaviour of a granular material is described using a new program MASOM based on Cundall's discrete element method. In the analysis the individual grains which make up the material are taken to be deformable 2D polygons of arbitrary size and shape. Contact forces between the grains are calculated according to Mindlin's solution for frictional contact between elastic bodies. The material in each grain is taken to be linear elastic but limited by the fracture strength of the material. Fracture is permitted along any one of a number of candidate fracture planes if an associated compressive load tending to split the gain reaches a critical level. Fragments of fractured grains are carried until they become too small to track using the explicit time integration algorithm used to advance the solution. The MASOM program is able to consider a number of different classes of elements and different types of contact between the various classes. Thus, in addition to the granular material the program can also model containers and loading devices. The program is used to simulate uniaxial and triaxial compression tests for geological materials. The results are shown to give results for stressstrain and stress difference versus pressure which are in qualitative agreement with test data. The numerical results reveal a very complex micromechanical behaviour in granular materials, including highly variable and rather unstable load paths and a very inhomogeneous load distribution within a representative sample of the material. A video of the response of a typical frictional material to applied loads shows an interesting localized effect near sample boundaries involving crowding together of grains which cannot be observed using conventional static field plots.