Overview Examples 1 Examples 2 Structures Moving nodes C-axis in Elle Euler angles in Elle Diffusion and mass transfer Elle-functions Elle command line options Basil Using basil


Elle - Project Overview

The aim of this project is to investigate a class of problems in structural geology and metamorphicpetrology where the kinetics of the deformation processes and metamorphic reactions involve similar time scales. It has proved extremely difficult to make much progress in experiments of deforming and reacting rocks or analogues, because the kinetics of the deformation processes cannot generally be simultaneously scaled with the kinetics of the reaction processes.

The investigation of deformation microstructures often assumes the dominance of a single deformation process, and this is no doubt in part because the theoretical framework for multi-process systems is still in its infancy (eg Karato 1987, Jessell & Lister 1990, Zhang et al. 1995). The interpretation of metamorphic assemblages generally takes into account the impact of deformation to distinguish different generations of minerals, on the other hand the role of deformation on the textures and mineralogy of a single assemblage is often hard to determine.

We are examining the link between the metamorphic and deformation histories of rocks and their microstructures by building a two-dimensional numerical simulation of the interaction between the grain scale processes involved in deformation and metamorphism.

METHODOLOGY

The development of a multi-process modelling system depends on three types of code being written: a common data format that describes all aspects of the geometry and attributes of the microstructures; micro-process based driving forces that determine the extent and direction of movement of nodes, and routines that actually enact the movement of nodes, and perform checks to ensure the coherence of the grain structure following these moves. The overall master program (including the data model) which will recursively parcel off tasks to each of the simulations to model specific micro-processes.

 

Figure 1. Program flow based on separate description of grain scale processes, in most cases building on existing and available software, with examples of output from these software. The model is essentially divided up into three elements: the dynamic calculations,that simulate the deformation mechanisms; the thermodynamic calculations, that simulate the chemical and surface energy driven processes; and the dynamic recrystallisation calculations, that simulate the formation new grains and the reorientation of crystal lattices. 

a) Data Structure

To combine existing programs and new algorithms together into an integrated numerical model, we have developed a data model which each of the existing programs can use as the base upon which it can calculate its appropriate deformation or metamorphic process. This data model can then be passed recursively or iteratively to each of the programs required for a particular numerical experiment.

The data model is based on the hierarchical division of the 2D space into grains, sub-grains and units.

 
Figure 2. Nodes represent points on grain, sub-grain or element boundaries. Each node may be joined to two other nodes (blue) or three other nodes (yellow). It is the movement of these nodes, and change in attributes at these nodes, that leads to changes in microstructure. Areas A & B are sub-grains of a larger grain, area C is a grain in its own right. 

The boundaries are defined as line segments joining neighbouring nodes, and it is the nodes that carry information about the local chemistry, mineralogy, mechanical properties and type of boundary. It is the movement of these nodes, and change in properties at these nodes, that results in changes in the microstructure of the sample.

For a typical simulation, the data model will be set up defining the initial microstructure, and then external stress or strain-rate boundary conditions, and a temperature history and fluid pressure will be applied. The deformation or metamorphic processes of interest can be then chosen, and the program  will pass the data model first to the program Basil to calculate the internal stresses within each grain and on each grain-boundary, and then the data model with the calculated stresses will be passed to the recrystallisation routines and the thermodynamic routines in turn.

b) Modelling of Micro-process driving forces

Wherever possible we have combined and built upon existing programs that simulate the driving forces for texture development. In particular the code for visco-elastic deformation behaviour will be modelled using an existing finite element program (Basil; Barr and Houseman, 1996). Programs that model dynamic recrystallization and lattice rotations (Jessell and Lister, 1990) and surface energy driving grain growth (Bons and Urai, 1992, and Bons 1994 unpublished) which have been developed at Monash and Utrecht are also available. Experience gained from the work of Zhang et al. 1994 suggests one possible route for the modelling of grain boundary sliding, although this remains a problematic area. The predictions of the equilibrium mineral and fluid assemblages will be accomplished using programs devloped by other research groups (eg. for mineral equilibria - Ge0-Calc, Brown et al., 1988; THERIAK, DeCapitani and Brown, 1987; and for fluids - EQ3NR, Wolery et al., 1993; EQBRM, Crerar, 1975, THERMOCALC, Powell & Holland, 1985).

c) Modelling of Micro-proccesses and Topology Checks

The treatment of inter- and intra-granular diffusion is being treated as the individual processes of nucleation, dissolution & transport. In many cases this leads to the creation, removal or change in position of nodes, and one of the more complicated aspects of the modelling system is the description of the movement of nodes, particularly the topology checks that need to be made to ensure that boundary intersections are correctly handled.
  

Figure 3. Topology checks. Once a node has moved, a series of checks have to be performed to ensure that boundaries do not intersect, and that grains have not disappeared.This figure shows a sub-set of the possible overlaps that need to be corrected. 

 

Figure 4. Triangulations of an arbitrary grain structure. a) Grain boundary structure, colours simply used to distinguish grains.The grains wrap around the horizontal and vertical edges. b) Delaunay triangulation using all boundaries and nodes. A Delaunay triangulation minimises the internal angles of all the triangles within a mesh, which provides relatively stable meshes for Finite Element calculations. c) Delaunay triangulation with the constraint that no triangle may have an internal angle of less than 30?.