  In this work we present a stellar structure model from
$f(\mathcal{R})$-gravity point of view capable to describe some classes of
stars (White Dwarfs, Brown Dwarfs, Neutron stars, Red Giants and the Sun). This
model was based on $f(\mathcal{R})$-gravity field equations for
$f(\mathcal{R})= \mathcal{R}+ f_2 \mathcal{R}^2$, hydrostatic equilibrium
equation and a polytropic equation of state. We compared the results obtained
with those found by the Newtonian theory. It has been observed that in these
systems, where high curvature regimes emerge, stellar structure equations
undergo modifications. Despite the simplicity of this model, the results were
satisfactory. The estimated values of pressure, density and temperature of the
stars are within those determined by observations. This
$f(\mathcal{R})$-gravity model has been proved to be necessary to describe
stars with strong fields such as White Dwarfs, Neutron stars and Brown Dwarfs,
while stars with weaker fields, such as Red Giants and the Sun, were best
described by the Newtonian theory.
