In any microstructure model of a random material, there are always two sources of error: statistical fluctuation and finite size effect [ 1, 15]. The first comes about because when constructing a model, there are many different choices of the random numbers possible that determine the arrangement of the phases. Each choice, in principle, can have different properties. This sensitivity to statistical fluctuation must be carefully tested. The second source of error, finite size-effect, comes about because the unit cell of the model can only contain a piece of the microstructure that is small compared to a experimental piece of the real material. One must ask the question: Is the model big enough so that its microstructure is typical of the real material [16, 17]?
In digital models, there is a third source of error: digital resolution. Arbitrary shapes are being represented by a collection of square or cubic pixels, and there will almost always be a dependence of properties on resolution. This can come about in two ways. Suppose one computes the properties of a composite made up of cubical particles that are randomly placed but oriented with the digital pixel axes. In this case, the shape of the particles is always represented properly, but the continuum elastic equations are discretized, so that there will still be an effect of resolution. If the particles were spheres, or cubes or bars that were not aligned with the digital pixel axes, the shape of the particles would then also change with resolution, adding to the digital resolution error. These sources of uncertainties will be discussed as we analyze the results of each model in the following section.