  The $f(R,T)$ gravity is an extended theory of gravity in which the
gravitational action contains general terms of both the Ricci scalar $R$ and
trace of the energy-momentum tensor $T$. In this way, $f(R,T)$ models are
capable of describing a non-minimal coupling between geometry (through terms in
$R$) and matter (through terms in $T$). In this article we construct a
cosmological model from the simplest non-minimal matter-geometry coupling
within the $f(R,T)$ gravity formalism, by means of an effective energy-momentum
tensor, given by the sum of the usual matter energy-momentum tensor with a dark
energy contribution, with the latter coming from the matter-geometry coupling
terms. We apply the energy conditions to our solutions in order to obtain a
range of values for the free parameters of the model which yield a healthy and
well-behaved scenario. For some values of the free parameters which are
submissive to the energy conditions application, it is possible to predict a
transition from a decelerated period of the expansion of the universe to a
period of acceleration (dark energy era). We also propose further applications
of this particular case of the $f(R,T)$ formalism in order to check its
reliability in other fields, rather than cosmology.
