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We present direct spectroscopic measurements of the broad 2175~{\AA}absorption feature in 505 star-forming main-sequence galaxies at $1.3\le z\le1.8$ using individual and stacked spectra from the zCOSMOS-deep survey.Significant 2175~{\AA} excess absorption features of moderate strength aremeasured, especially in the composite spectra. The excess absorption is welldescribed by a Drude profile. The bump amplitude expressed in units of$k(\lambda)=A(\lambda)/E(B-V)$, relative to the featureless Calzetti et al.law, has a range $B_k\approx0.2\textrm{--}0.8$. The bump amplitude decreaseswith the specific star formation rate (sSFR), while it increases moderatelywith the stellar mass. However, a comparison with local "starburst" galaxiesshows that the high-redshift main-sequence galaxies have stronger bumpfeatures, despite having a higher sSFR than the local sample. Plotting the bumpstrength against the $\Delta\log\mathrm{sSFR}\equiv \log \left(\mathrm{SFR}/\mathrm{SFR_{MS}}\right)$ relative to the main sequence, however,brings the two samples into much better concordance. This may indicate that itis the recent star formation history of the galaxies that determines the bumpstrength through the destruction of small carbonaceous grains by supernovae andintense radiation fields coupled with the time delay of $\sim1~\mathrm{Gyr}$ inthe appearance of carbon-rich asymptotic giant branch stars.

The 2175 {\AA} dust feature in star-forming galaxies at $1.3\le z\le 1.8$: the dependence on stellar mass and specific star formation rate