  We have performed a series of chemodynamical simulations of barred disc
galaxies. Our goal is to determine the physical processes responsible for the
increase in the central gas-phase metallicity and of the central SFR observed
in SDSS. We define a 2kpc diameter central aperture to approximate the
integrated spectroscopic fibre measurements from the SDSS. The chemical
evolution observed within this central region depends critically upon the
relative size of the bar and the aperture, which evolves strongly with time. At
t~0.5Gyr, a strong bar forms, whose length is considerably longer than the 2kpc
aperture. The stars and gas lose angular momentum and follow elongated orbits
that cause an intense mixing of the gas between the central region and its
surroundings. During the next 1.5Gyr, the orbits of the gas contract
significantly until the entire gas bar is contained in the 2kpc aperture,
resulting in a net flux of gas into the central region. During this period, the
metallicity in the central region increases steadily, and this enrichment is
dominated by metal-rich gas that is flowing into the central region. The main
result of this work is therefore that the observed enrichment in the centres of
barred galaxies is not dominated by in-situ enrichment by stars formed in the
centre. Rather, star formation occurs along the full length of the bar, much of
which occurs initially outside the 2kpc aperture. About 50% of the metals that
end up in the central region originate from this extended bar-long star
formation, but flow into the central region due to loss of angular momentum. We
conclude that there is no direct connection between central SFR and central
metallicity. The central metallicity does not originate exclusively from
central stars. Instead, the global SFR (especially along the bar) and the
large-scale flow of enriched gas play a major role.
