  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).
