  This paper compares the chemical evolution of the Large Magellanic Cloud
(LMC) to that of the Milky Way (MW) and investigates the relation between the
bar and the inner disc of the LMC in the context of the formation of the bar.
We obtained high-resolution and mid signal-to-noise ratio spectra with
FLAMES/GIRAFFE at ESO/VLT and performed a detailed chemical analysis of 106 and
58 LMC field red giant stars (mostly older than 1 Gyr), located in the bar and
the disc of the LMC respectively. We measured elemental abundances for O, Mg,
Si, Ca, Ti, Na, Sc, V, Cr, Co, Ni, Cu, Y, Zr, Ba, La and Eu. We find that the
{\alpha}-element ratios [Mg/Fe] and [O/Fe] are lower in the LMC than in the MW
while the LMC has similar [Si/Fe], [Ca/Fe], and [Ti/Fe] to the MW. As for the
heavy elements, [Ba,La/Eu] exhibit a strong increase with increasing
metallicity starting from [Fe/H]=-0.8 dex, and the LMC has lower [Y+Zr/Ba+La]
ratios than the MW. Cu is almost constant over all metallicities and about 0.5
dex lower in the LMC than in the MW. The LMC bar and inner disc exhibit
differences in their [{\alpha}/Fe] (slightly larger scatter for the bar in the
metallicity range [-1,-0.5]), their Eu (the bar trend is above the disc trend
for [Fe/H] > -0.5 dex), their Y and Zr, their Na and their V (offset between
bar and disc distributions). Our results show that the chemical history of the
LMC experienced a strong contribution from type Ia supernovae as well as a
strong s-process enrichment from metal-poor AGB winds. Massive stars made a
smaller contribution to the chemical enrichment compared to the MW. The
observed differences between the bar and the disc speak in favour of an episode
of enhanced star formation a few Gyr ago, occurring in the central parts of the
LMC and leading to the formation of the bar. This is in agreement with recently
derived star formation histories.
