Rigidity and conductivity percolation thresholds in particulate composites

Abstract

Percolation threshold criteria for particulate composites are derived in terms of the average coordination number in the percolating cluster using the constraint theory of Phillips and Thorpe. Rigidity percolation threshold value depends on the nature of bonding at the contacts between particles. In the absence of any bonding at the contacts, the average coordination number at the rigidity percolation threshold is six. For completely bonded contacts, it is shown that the rigidity percolation threshold is equal to the conductivity percolation threshold and, in three-dimensions, the average coordination number at the threshold is 2.4 (2 in two-dimensions). The threshold criteria are converted to the number and the volume fractions of the percolating phase and the results are compared with available data. Results are also obtained for threshold values in continuum matrix composites.