Recently, several studies have shown that young, open clusters are characterized by a considerable overabundance in their barium content. In particular, D'Orazi et al. reported that in some younger clusters [Ba/Fe] can reach values as high as ~0.6 dex. The work also identified the presence of an anticorrelation between [Ba/Fe] and cluster age. For clusters in the age range ~4.5 Gyr-500Myr, this is best explained by assuming a higher contribution from low-mass asymptotic giant branch stars to the Galactic chemical enrichment. The purpose of this work is to investigate the ubiquity of the barium overabundance in young stellar clusters. We analysed high-resolution spectroscopic data, focusing on the s-process elemental abundance for three nearby young associations, i.e. AB Doradus, Carina-Near and Ursa Major. The clusters have been chosen such that their age spread would complement the D'Orazi et al. study. We find that while the s-process elements Y, Zr, La and Ce exhibit solar ratios in all three associations, Ba is overabundant by ~0.2 dex. Current theoretical models cannot reproduce this abundance pattern; thus, we investigate whether this unusually large Ba content might be related to chromospheric effects. Although no correlation between [Ba/Fe] and several activity indicators seems to be present, we conclude that different effects could be at work which may (directly or indirectly) be related to the presence of hot stellar chromospheres.