This paper presents a three dimensional wave propagation model of an aluminum lug joint specimen with piezoelectric sensors and actuators. The goal is to quantify Lamb wave reflections and mode conversions caused by complex material boundaries and damage. The numerical analysis comprises a combination of the local interaction simulation approach (LISA) and the sharp interface model (SIM). In this paper, three cases studies are presented. The simulation is conducted on three aluminum lug joints: a healthy (i.e. undamaged) lug joint, a lug joint with a single 10 mm crack located at a structural hot spot, and a lug joint with a single 20 mm crack located at a structural hot spot. The matching pursuit decomposition (MPD) algorithm is used to decompose each Lamb wave mode in the time-frequency domain. Numerical results are presented, which are also validated with experimental results. The results demonstrate that the model is capable of detecting the presence of damage in geometrically complex metallic aerospace components through mode conversion analysis.