Cement-based materials exhibit very complex structures over many length scales. For example, concrete is a composite material, containing rocks and sand (coarse and fine aggregates) as inclusions in a cement paste matrix. The effective properties of this composite material are complicated, even if we consider the cement paste matrix to be a simple, homogeneous material. Coarse aggregate size is on the order of 1 to 20 millimeters, while the fine aggregate size typically ranges from 0.2 to 2.0 millimeters. Thus the aggregates alone span two orders of magnitude is size.
Now consider the cement paste matrix. It is not a simple, homogeneous material. Instead, cement paste is formed from an original water:cement particle mixture, which forms a dense suspension with complex viscoelastic properties. The cement particles cover a size range of about 0.001 to 0.1 millimeters, and each particle is itself a complex agglomeration of several different calcium silicate, aluminate, ferrite, and sulfate phases. When the cement particles are suspended in water, hydration reactions begin, forming both crystalline and amorphous reaction products that fill in the pore space and eventually change the viscoelastic suspension into a rigid solid. When hydration is essentially complete, pores exist on length scales ranging from 106 millimeters (1 nm) in one of the amorphous reactants, up to 0.0001- 0.01 millimeters in the capillary pore space. Therefore, the important length scales in concrete range from about 106 millimeters up to about 20 millimeters - 7 orders of magnitude!
The fundamental idea of materials science is the triad of processing, microstructure, and properties, and their interrelationships. For a given material, experimental and theoretical understanding of this triad is necessary in order to have true control of the material and its properties. The complexity of cement-based materials rule out much hope of using analytical methods to achieve theoretical understanding of, say, microstructure-property relationships. This forces us to consider how computational materials science techniques can be used.
In the context of cement-based materials, computational materials science means: 1) using a computer to build, via computer simulation, a numerical microstructure that is realistically based on individual cement particles and their hydration products, and 2) operating on the completed microstructure with various algorithms to exactly compute, within numerical precision, the physical properties of interest (electrical conductivity, elastic moduli, fluid permeability, etc.). The computed properties are then compared to experimental results. Agreement leads to new understanding of microstructure-property relationships, since the numerical microstructure model is available for analysis. Disagreement leads to refinement of the microstructure model, to try to find where it does not agree with real microstructures.
For such an approach, some general unifying ideas for random systems are extremely important. For example, the ideas of percolation theory have proven to be extremely useful in describing and understanding microstructural development and microstructure-property relationships in cement-based materials [1,2].
In light of the above discussion, the computer exercises that will be described below cover both microstructure models and percolation theory. In addition, there is one simple application exercise that performs a computation on a given microstructure. Most of the algorithms that compute properties require very fast workstations or supercomputers to execute in a reasonable amount of time. As these exercises have been designed to be executed on microcomputers, the simulation exercises have been scaled down in order to run more quickly. There are four exercises described in this module, which have been adapted from the exercises used at several of the ACBM/NIST Computer Modelling Workshops.