The research undertaken from 2004-2009 to launch this suite of technology has its roots in the relatively young field of computational mechanics of discontinua. A significant additional effort working in the field of computational fluid mechanics has also been necessary to prepare for challenging fluid-structure interaction modelling.
Here, in the technology section, while implicitly acknowledging the long history of previous developments in these fields, we aim to provide a brief outline emphasising only the core technologies that have been added during the 2004-2009 VGW project. First, we provide a background to discrete system modelling and code developments.
History of Computational Mechanics of Discontinua
Discrete Element Methods (DEM) and Discontinuum Deformation Analysis (DDA) were the first computational tools for discontinua simulation. They were developed by researchers from various disciplines (notably P. Cundall, G. Shi, J. Williams and G. Mustoe, C Thornton) in the 1970’s and 1980’s. DEM is well suited for dynamic systems, uses contact detection algorithms, contact force algorithms and applies a time integration scheme to simulate the Newtonian mechanics of these multi-body problems. DDA deals mostly with quasi-static blocky systems, is a displacement-based method typically applied to jointed rock masses and employing an implicit integration scheme. Both are based on rigid or semi-deformable particles.
During deposition of particles, for example, DEM can track motions and reveal all the dynamic behaviour until eventually the particles all come to a state of rest. The static particulate then takes on emergent properties such as shear strength, porosity and permeability, and these may vary locally. Each property is the result of every single particle’s experience of interaction forces up to that moment.
In practice, and especially when particles are of non-spherical geometry and of a wide particle size distribution, local grain-scale phenomena are of crucial importance in affecting the whole particulate system under consideration. The averaged continuous properties assumed for continuum methods (e.g. CFD, FEM) are therefore not applicable. CFD methods are generally poor in describing the particulate flow stage, i.e. whilst the particulate behaviour is fluid-like. FEM methods are poor at describing the deformability or stability of the at-rest particulate pack of solids, e.g. at a stage when further stressed or disturbed. The capabilities of the DEM approach make it an attractive tool to accommodate both fluid-like and solid-like properties of particulates. Furthermore, as hardware performance becomes increasingly powerful, more challenging problems of discontinua can be addressed. This explains why the computational mechanics of discontinua is a fast growing field and why DEM is now considered a “must have” technology by many groups of research scientists and engineers.
Combined FEMDEM modelling (A. Munjiza 1990, PhD Swansea University )
One of the most powerful developments in DEM that began in the late 1980’s is the combination of FEM and DEM. Decades of FEM modelling technology designed for modelling stressed and deformed solids has now been combined with the motion-tracking capability of DEM. Combined FEMDEM was first proposed by A. Munjiza and the first working FEMDEM code (the RG program written in C++) was developed by Munjiza in 1990. Originally, combined FEMDEM incorporated finite strain elasticity-plasticity coupled with a smeared crack model for fracture and fragmentation. This was later combined with compressible fluid coupling dealing with the explosive gas pressure that extends the cracks of fracturing and fragmenting solids e.g. during rock blasting. Combined FEMDEM allows the individual particle behaviour governed by DEM formulations (particle detection and interaction) to be combined with an ability to discretise any particle into considerably smaller deformable finite elements. Important advantages over DEM models based on spheres, ellipsoids or even superquadrics are that complex particle shapes can be introduced. Furthermore, a vast range of alternative e.g. non-linear constitutive or internally fracturing properties can be introduced for the individual particles, with the additional advantages of being able to add further field variables such as temperature. Thus, if stresses are sufficient to propagate cracks and initiate failure in the particles, they will fragment and the DEM formulations will continue to track the fragment motions. Such FEMDEM approaches have been successfully applied to modelling the key processes of stress wave propagation and expanding gas-driven fragmentation in Rock Blasting.
Key Developments 1995-2004
Key developments from 1995-2004, lead by Prof Munjiza at QMUL, have enabled the modelling of simple systems approaching one billion particles and set the foundations for large systems of complex-shaped particles to be simulated with greater accuracy. These are summarized as follows:
- The development of the family of linear contact search algorithms starting with NBS (no binary search)
- Introduction of discretized contact elements and distributed contact force with penalty function – for use with FEMDEM
- Introduction of integration solution for finite rotation in 3D of irregular-shaped bodies
- Introduction of a compressible gas flow model coupled with fracture and fragmentation
- Code parallelisation using dynamic domain decomposition
- Illustration of a rational 3D dynamic packing simulation for particles with edges, faces and corners using cubes with rigid interiors and deformable outer skin thickness
Early Simulations (2000) by Prof Munjiza (QMUL), in collaboration with Dr Latham (ICL)
Results from a collaborative EPSRC project (QMUL/IC) entitled “The Packing of Rock Fragments” and employing the combined FEMDEM method and code of Prof Munjiza are presented here as simulations.
Furthermore, these developments were extended into the realm of practical geoscience and geo-engineering at Imperial College by Dr Latham and co-workers, from 2000-2004, for example by:
- Programme of experimental validation of the simulation of cube packing
- Introduction of realistically-shaped particles into discontinuum modelling using 3D laser scanning of rock aggregates
These highlighted the range of particulate systems and problems that geoscientists and geoengineers could address with FEMDEM. Sophisticated 2D simulations with deformability and fracture had been demonstrated. 3D simulations were well developed for arbitrary shape but lacked an ability to handle fully deformable multi-body interactions.
In 2004 the text-book “The Combined Finite-Discrete Element Method ” by Antonio Munjiza, was published by Wiley New York. The arrival of this authoritative text-book with its comprehensive treatment of Munjiza’s key algorithmic developments and illustrated outputs, provides a suitable baseline from which the further achievements of the VGW project and VGeST can now be seen.