  The chemical enrichment in the interstellar medium (ISM) of galaxies is
regulated by several physical processes: stellar evolution, grain formation and
destruction, galactic inflows and outflows. Understanding such processes is
essential to follow the chemical enrichment of galaxies through the cosmic
epochs, and to interpret the observations. Despite the importance of such
topics, the efficiency of the different processes driving the evolution of
baryons in galaxies, remain controversial. We revise the current description of
metal and dust evolution in local low-metallicity dwarf galaxies and we develop
a description for Lyman Break Galaxies. Our main goal is to reproduce i) the
peak in the mass of dust over the mass of stars (sMdust) observed within few
hundred Myrs; ii) the decrease of the sMdust at later time. The spectral energy
distribution of the galaxies is fitted with the "Code Investigating GALaxies
Emission" (CIGALE), through which the stellar and dust masses, and the star
formation rate are estimated. For some of the dwarf galaxies, the metal and gas
content are also available. We run different calculations of chemical evolution
in galaxies, and we fit the observed properties through the model predictions.
We show that i) a top-heavy initial mass function that favours massive stars
and a dust condensation fraction for Type II Supernovae (SNe II) of 50% or more
help to reproduce the peak of sMdust observed after 100 Myrs since the
beginning of the cycle; ii) galactic outflows play a crucial role in
reproducing the decline in sMdust with age, and they are more efficient than
grain destruction from SNe II; iii) a star formation efficiency (mass of gas
converted into stars) of few per cent is required to explain the metallicity of
local dwarf galaxies; iv) dust growth in the ISM is not necessary to reproduce
the sMdust and, if present, its effect is erased by galactic outflows.
