  Silicon pixel detectors are at the core of the current and planned upgrade of
the ATLAS experiment at the LHC. Given their close proximity to the interaction
point, these detectors will be exposed to an unprecedented amount of radiation
over their lifetime. The current pixel detector will receive damage from
non-ionizing radiation in excess of $10^{15}$ 1 MeV ${n}_{eq}/{cm}^2$, while
the pixel detector designed for the high-luminosity LHC must cope with an order
of magnitude larger fluence. This paper presents a digitization model
incorporating effects of radiation damage to the pixel sensors. The model is
described in detail and predictions for the charge collection efficiency and
Lorentz angle are compared with collision data collected between 2015 and 2017
($\leq 10^{15}$ 1 MeV ${n}_{eq}/{cm}^2$).
