This study implements key mechanisms and parameters observed from the previous compression after impact (CAI) experimental studies into finite element models, to study their effects parametrically on residual compression strength. The mechanisms and parameters include: impact damage area, the role of intact interfaces within the overall damaged region (identified here as the "undamaged cone"), interlaminar toughness, and the extent of permanent out-of-plane deformation. The findings highlight that within the limits observed experimentally, in addition to the size of the damaged area, interlaminar toughness and the extent of permanent out-of-plane deformation strongly affect CAI strength (by up to ~100% for a given damage area), with toughness playing a more significant influence than permanent out-of-plane deformation. For the first time, and contrary to much of the literature, the significant role of the undamaged cone is evidenced and quantified.