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(abridged) We explore the Frontier Fields cluster MACS J0416.1-2403 atz=0.3972 with VIMOS/VLT spectroscopy from the CLASH-VLT survey covering aregion which corresponds to almost three virial radii. We measure fluxes of 5emission lines of 76 cluster members enabling us to unambiguously derive O/Hgas metallicities, and also SFRs from Halpha. For intermediate massses we finda similar distribution of cluster and field galaxies in the MZR and mass vs.sSFR diagrams. Bulge-dominated cluster galaxies have on average lower sSFRs andhigher O/Hs compared to their disk-dominated counterparts. We use the locationof galaxies in the projected velocity vs. position phase-space to separate ourcluster sample into a region of objects accreted longer time ago and a regionof recently accreted and infalling galaxies. We find a higher fraction ofaccreted metal-rich galaxies (63%) compared to the fraction of 28% ofmetal-rich galaxies in the infalling regions. Intermediate mass galaxiesfalling into the cluster for the first time are found to be in agreement withpredictions of the fundamental metallicity relation. In contrast, for alreadyaccreted star-forming galaxies of similar masses, we find on averagemetallicities higher than predicted by the models. This trend is intensifiedfor accreted cluster galaxies of the lowest mass bin, that displaymetallicities 2-3 times higher than predicted by models with primordial gasinflow. Environmental effects therefore strongly influence gas regulations andcontrol gas metallicities of log(M/Msun)<10.2 (Salpeter IMF) cluster galaxies.We also investigate chemical evolutionary paths of model galaxies with andwithout inflow of gas showing that strangulation is needed to explain thehigher metallicities of accreted cluster galaxies. Our results favor astrangulation scenario in which gas inflow stops for log(M/Msun)<10.2 galaxieswhen accreted by the cluster.

CLASH-VLT: Strangulation of cluster galaxies in MACSJ0416.1-2403 as seen from their chemical enrichment