One major conclusion of this work is that simple digital models made with elongated objects, in this case rectangular parallelipiped bars, can illustrate many of the pertinent features of real porous materials made up of interlocking crystals. Digital models have great flexibility, and certainly much more can be done with them to help illuminate experimental questions than has been done in the present study. The computational procedures needed to study these models have been laid out in this paper, along with the appropriate averaging equations for configurational and rotational averages.
To accurately use digital models for random systems, one must quantify and minimize the error associated with statistical fluctuation, finite size effect, and digital resolution. Away from the percolation threshold, the first two are usually much less than the digital resolution error. As the percolation threshold is approached, the statistical fluctuation and finite size effect errors grow quickly. But the digital resolution error grows somewhat as well, remaining the controlling error. This is because increasingly small "bridges" of material hold the porous composite together as the percolation threshold is approached, causing increasingly larger resolution errors.
For porosities away from the percolation threshold, the stiffness of the connecting or overlap material between bars played a large role in determining the elastic modulus. For the 2-D models, the dependence of the overall moduli on the stiffness of the overlap regime seemed to be fairly insensitive to microstructure.
Another key finding was that to reproduce 3-D experimental results, it is crucial to use 3-D models. There are important differences in connectivity between 2-D slices and the 3-D models from which they came. These differences cannot be accounted for by using some kind of 2-D version of the 3-D solid elastic moduli in the 2-D solid backbone, although this procedure should become more accurate at lower porosities. Qualitatively, there are some similarities (see Fig. 12), but there is nothing close to quantitative agreement. Building better 3-D models for interlocking crystal porous materials must then be the focus of future work. In particular, how the moduli approach the zero moduli limit is a crucial test case for any 3-D model. Matching the apparent percolation threshold of experimental systems will be of major importance in this task.