Frictional energy dissipation in materials containing cracks

Kachanov's simplified model of microcrack interaction is applied to an investigation of the behaviour of a cracked body under predominantly compressive periodic loading, so that the cracks experience periods of closure and slip, with frictional dissipation. The model is shown to be equivalent to a discrete elastic frictional system with each crack representing one node. Theorems and algorithms from such systems are applied to determine the conditions under which the system shakes down to a state with no slip and hence no energy dissipation in friction. For conditions not too far beyond the shakedown state, the dissipation is significantly affected by the initial conditions, but with larger oscillating loads, it becomes a unique and increasing function of load amplitude. The effect of crack interaction is assessed by comparison with an uncoupled model, for which the dissipation is obtained as a summation of closed form expressions over the crack population. For small numbers of cracks, the results are significantly dependent on the randomly chosen crack locations and sizes, but with larger populations, a statistically significant decrease in dissipation is observed with increasing interaction terms.