  In the realm of massive stars, strong binary interaction is commonplace. One
extreme case are overcontact systems, which is expected to be part of the
evolution of all stars evolving towards a merger, and is hypothesized to play a
role in the formation of binary black holes. However, important simplifications
are made to model the evolution of overcontact binaries, namely that tidal or
rotational deformation is frequently ignored. Yet, both observation and theory
show that overcontact stars are heavily tidally deformed, leaving a potentially
important effect on the outer layers unaccounted for in models. In this work we
develop the methodology to represented tidally deformed stars. Using numerical
methods, we compute the structure correction factors to the 1D spherical
stellar structure equations due to the binary Roche potential, and compare them
to existing results and the structure corrections of single rotating stars. We
implement the new structure correction factors into the stellar evolution code
MESA and explore several case studies. We compare the differences between our
simulations when no rotation is included, when we treat rotation using single
star corrections (i.e. only accounting for centrifugal deformation) or when we
use tidal deformation. We find that ignoring rotation in deformed detached
eclipsing binaries can produce a radius discrepancy of up to 5%. The difference
between tidal and single star centrifugal distortion models is more benign at
1%, showing that single rotating star models are a suitable approximation of
tidally deformed stars in a binary system. In overcontact configurations, we
find a similar 5% variation in surface properties as a result of tidal
distortion with respect to non-rotating models, showing that it is
inappropriate to model binary stars that fill their Roche lobe significantly,
as non-rotating.
