This paper concerns with the local connectivity (i.e., the probability of node isolation) of wireless networks with directional antennas. We propose an analytical framework to study the local connectivity with the consideration of directional antenna models and various channel conditions. With the framework, we construct a novel directional antenna model called Iris. We show that Iris can better approximate realistic directional antennas and can be easily used to analyze the local connectivity compared with existing directional antenna models. Extensive simulations show that the theoretical results are in good agreement with the simulation results verifying the accuracy and the effectiveness of our analytical framework.