There are two general methods used to actually simulate microstructure in a computer. By simulate we mean that in some way, at any position in the space considered by the model, it is known what material phase, solid or porosity, exists at that point. These two methods are the continuum and digital-image-based methods. Both are used in the computer modelling of ITZ microstructure, and are complementary.
In a continuum model, one thinks of particles embedded in a matrix. Each solid particle is represented as a simple geometrical shape (such as a sphere or an ellipsoid) and is characterized by its centroid location, dimension, and orientation. For a sphere, this requires only the (x,y,z) coordinates of the sphere center and its radius. For an ellipsoid, in addition to the centroid coordinates, the lengths of the three semiaxes are required, along with three angles describing the orientation of the ellipsoid [4]. Particles following a representative particle size distribution are placed into a three-dimensional computational volume in a random configuration according to some placement statistics. A common way of placing particles is that the particles do not overlap. This covers the case of aggregates in concrete, or cement particles in water. To accomplish this kind of placement, particles to be placed must be checked for overlap with existing particles. If an overlap exists, the new particle is removed and placed randomly elsewhere. Checking for the overlap of two spherical particles, given their centroids and radii, is computationally trivial. The center of two particles may not come closer than the sum of their radii. Examining the overlap of two general ellipsoids is mathematically more challenging, but still tractable [4,5].
The major advantage of a continuum approach is that the memory requirement for representing a relatively large volume of material is small. For example, concretes containing on the order of one million aggregate particles have been simulated using this approach [6], since only four (for spheres) and nine (for tri-axial ellipsoids) million numbers need to be stored for this size system. This gives a total computer memory requirement of 32-72 MBytes (at eight bytes per number or about 16 significant figures), which is not a large amount of memory for modern computers.
In a digital-image-based model, the computational volume is subdivided into a three-dimensional array of individual cubic elements, typically called pixels or voxels. Here, each cement or aggregate particle can be composed of many pixels. In this way, complex shapes and phase distributions which defy simple geometric descriptions can be represented at finite resolution. When a complex random process like hydration is considered, with the microstructure undergoing re-distribution of material and the random growth of new phases, a digital-image-based method becomes absolutely necessary to capture what is happening in the microstructure. For modelling cement paste, the resolution typically employed is on the order of 1 µm / pixel. After approximating the initial configuration of multi-size, multi-phase cement particles in water, cellular automata techniques are employed to simulate the hydration reactions and developing microstructure in three dimensions [7,8]. Rules which maintain the appropriate volume stoichiometry have been developed and implemented for the dissolution, diffusion, and reaction of the starting cement clinker phases as detailed in Refs. [7,8].