It is important to know from where the ideas behind the computational materials science of concrete came. There were four main intellectual sources for these ideas. First is the work on the structure of amorphous semiconductors like silicon and germanium in the 1960s and 1970s. Physicists could do crystal physics calculations on periodic crystals; however, the problem of amorphous semiconductors was entirely different. If there was no underlying crystal lattice, how was one to do any calculations at all? Analytical approximations were tried, with only a limited degree of success (Zallen, 1983). Then models were built, where several hundred atoms were represented by a computer simulation model. Algorithms were applied to these models to compute properties, which were then used in an attempt to explain experimental results.
The second and third sources were two highly innovative developments in the materials science of concrete community, both in the 1980s, which appeared to be unrelated to the previous amorphous semiconductor work, but which in fact were similar to it. Wittmann, Roelfstra, and Sadouki published two important papers on numerically simulating the structure and properties of concrete in 2-D (Wittmann and others, 1984; Roelfstra and others, 1985). Simple models were developed for simulating the shape and arrangement of aggregates in concrete. A finite element grid was applied to these models in order to compute properties like thermal conductivity and elastic moduli. Then, independently, Jennings and Johnson published work on a three-dimensional (3-D) model of cement paste microstructure development for C3S pastes (Jennings and Johnson, 1986). This effort carried the development of computational materials science down to the micrometer scale of cement. Various sized particles, which followed a real cement particle size distribution, were dispersed randomly in 3-D. Rules were applied to these continuum spherical particles to simulate the dissolution of cement and the growth of hydration products.
The fourth intellectual source was a paper showing how a random walk algorithm could be applied to continuum models to compute electrical and diffusive transport in their pore space (Schwartz and Banavar, 1989). While trying to apply this algorithm to Jennings' cement paste model, since it was a continuum model, we experimented with digitizing the microstructure of simple models and then using random walks on the digital lattice. The combination of the ideas of random walks, digital images, and a cement paste hydration microstructure development model led directly to the first NIST cement paste hydration model. The subsequent realization that any finite element or finite difference algorithm would work on a digital lattice allowed almost any physical property to be computed and so greatly increased the ability of the cement paste model to produce predictions that were directly comparable to experimental results.
It should be mentioned that other kinds of random structure models grew popular around the same time, like the diffusion-limited aggregation (Meakin, 1988) and Eden models (Eden, 1961). All these kinds of models have similarities, except that actual cement chemistry is built into the cement hydration model. These other two models are examples of rule-based or cellular automaton models where the rules are chosen somewhat arbitrarily, and not always in close company with some known physics or chemistry (Wolfram, 1986; Young and Corey, 1990), even though physically realistic behavior is often seen.