  In this study one resorts to the phenomenology of models endowed with a
non-minimal coupling between matter and geometry, in order to develop a
mechanism through which dynamics similar to that due to the presence of dark
matter is generated. As a first attempt, one tries to account for the
flattening of the galaxy rotation curves as an effect of the non-(covariant)
conservation of the energy-momentum tensor of visible matter. Afterwards, one
assumes instead that this non-minimal coupling modifies the scalar curvature in
a way that can be interpreted as a dark matter component (albeit with negative
pressure). It is concluded that it is possible to mimic known dark matter
density profiles through an appropriate power-law coupling $f_2 = (R/R0)^n$,
with a negative index $n$ -- a fact that reflects the dominance of dark matter
at large distances. The properties of the model are extensively discussed, and
possible cosmological implications are addressed.
