Keywords: discontinuous modelling, discrete element method.

Computational modelling of particulate and inherently discontinuous solids may often not be adequately dealt with by a homogenised, continuum description and the discrete nature of discontinuities needs to be taken into account. Such analyses usually concern a system of multiple bodies or particles (rigid or deformable), which are potentially coming into contact as the solution progresses and the bodies to be considered can in general be of arbitrary shapes. The solution evolves in time and is typically treated as a dynamic problem, which may or may not have a steady state solution.

Furthermore, most media can (or indeed need to) be treated as discontinuous at some level of observation below macro, as the scale of the problem becomes similar to the characteristic length scale of the associated material structure, and the interaction laws between bodies or particles need to be invoked instead of continuum constitutive laws. Many discontinuous modelling frameworks are increasingly moving towards formulations and applications in multi field and multi physics problems, in particular in the area of the coupled fluid flow in discontinuous, jointed media.

It will be demonstrated that there are many similarities and unifying aspects between the seemingly different discontinuous modelling frameworks (Discrete Element Method DEM [1], Combined DEM/FEM [3,5], MDEM Modified Distinct Element Method, Discontinuous Deformation Analysis DDA [2], Non Smooth Contact Dynamics NSCD [4]) in the manner they deal with the characterisation of bodies geometry and contact detection, with the imposition of contact constraints and boundary conditions, with the definition and description of bodies deformability, fracturing and fragmentation, the transition from continua to discontinua and the associated time stepping algorithms.

It will be further argued that discontinuous modelling frameworks offer exciting modelling opportunities, especially in the context of fragmentation problems as well as in the microscopic simulations of the behaviour of heterogeneous materials, where simpler constitutive laws applied at the micro, meso or nano level, directly generate manifestations of complex macroscopic constitutive behaviour.

Increased computing power and efficient contact detection algorithms are likely not only to allow modelling of progressive fracturing, including fragmented state, but will also enable further development and enhancement of discrete micro structural models of material behaviour, where the continuum concept may be partially abandoned and an internal length scale may be intrinsically incorporated into the model, e.g. discrete-continuum models [6,7]. Moreover, the large scale simulations with adaptive multi scale material models, where different regions or domains are accounted for at a different scale of observation seem possible in a not-too-distant future.

1

P.A. Cundall and R.D. Hart, "Numerical Modelling of Discontinua", Engineering Computations, 9: 101-114, 1992. doi:10.1108/eb023851

2

G.H. Shi, "Block System Modelling by Discontinuous Deformation Analysis", Computational Mechanics Publication, Southampton, 1993.

3

A. Munjiza, D.R.J. Owen, N. Bicanic, "A Combined Finite/Discrete Element Method in Transient Dynamics of Fracturing Solids", Engineering Computations, 12: 145-174, 1995. doi:10.1108/02644409510799532

4

M. Jean, "The non-smooth contact dynamics method", Computer Methods in Applied Mechanics and Engineering, 177: 235-257, 1999. doi:10.1016/S0045-7825(98)00383-1

5

A. Munjiza, The Combined Finite-Discrete Element Method, John Wiley & Sons, London, 2004. doi:10.1002/0470020180

6

J. Fish, "Discrete to Continuum Multiscale Bridging", Multiscaling in Molecular and Continuum Mechanics: Interaction of Time and Size from Macro to Nano, G.C. Sih (ed), Springer-Verlag, 2006.

7

N. Bicanic, Discrete Element Methods, Chapter 11, Vol 1 Fundamentals, Encyclopedia of Computational Mechanics, John Wiley & Sons, 2007.

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