Using high-resolution Hubble Space Telescope imaging data, we perform a visual morphological classification of $sim 36,000$ galaxies at $z < 1$ in the DEVILS/COSMOS region. As the main goal of this study, we derive the stellar mass function (SMF) and stellar mass density (SMD) sub-divided by morphological types. We find that visual morphological classification using optical imaging is increasingly difficult at $z > 1$ as the fraction of irregular galaxies and merger systems (when observed at rest-frame UV/blue wavelengths) dramatically increases. We determine that roughly two-thirds of the total stellar mass of the Universe today was in place by $z sim 1$. Double-component galaxies dominate the SMD at all epochs and increase in their contribution to the stellar mass budget to the present day. Elliptical galaxies are the second most dominant morphological type and increase their SMD by $sim 2.5$ times, while by contrast, the pure-disk population significantly decreases by $sim 85%$. According to the evolution of both high- and low-mass ends of the SMF, we find that mergers and in-situ evolution in disks are both present at $z < 1$, and conclude that double-component galaxies are predominantly being built by the in-situ evolution in disks (apparent as the growth of the low-mass end with time), while mergers are likely responsible for the growth of ellipticals (apparent as the increase of intermediate/high-mass end).
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