Elasticity and criticality in pruned prestressed disordered networks

Unstressed disordered central-force spring networks are stable above and floppy below a critical coordination given by the Maxwell isostaticity criterion. It has been shown that one can tune the Poisson ratio of such networks to any value in its allowed range by selectively pruning a small fraction of the bonds as one approaches the limit of mechanical stability. Here we ask how tuning the Poisson ratio by pruning bonds is altered by the existence of prestresses on the network. We show that the response to pruning is altered completely and that the degree of tunability is highly influenced by the nature of the prestress.