Abstract
In this study we have modeled grains in rocks as infinite arrays of polygonal prisms and studied the stress distribution in these models under two dimensional pressure. The principal result is that in rocks under pressure, even for high moduli contrast, the fraction of material that is subject to significant stress concentrations due to sharp grain boundaries is very small. We also find that the overall moduli of the composite materials fall within the Hashin bounds. Plausible variations in the model yield overall moduli that span more than 98 percent of the bounds. Additional problems are mentioned.
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