A Microcrack Model of Dilatancy in Brittle Materials

For a solid containing preexisting flaws, overall nonlinear constitutive relations are developed on the basis of a model which endows a preexisting flaw with frictional and cohesive resistance, and which includes nucleation and growth of tension cracks at the preexisting flaw, as it deforms under the action of an overall compressive load. The preexisting flaws may be randomly distributed or may have an initial preferential distribution. They may be of varying sizes and orientations. Even when the flaws are randomly distributed, their preferential activation, and the nucleation and growth of tension cracks at preferential flaws, render the overall response of the solid highly anisotropic. As a first step toward a more complete constitutive micromechanical modeling, a dilute distribution of preexisting flaws is assumed, rate constitutive relations are developed for loading and unloading, which include hysteresis, dilatancy, and other characteristics observed experimentally in rocks, ceramics, concrete, and similar brittle materials. A number of illustrative examples are worked out, and the results are compared to relevant experimental observations.