  Dark energy models based on f(R) theory have been extensively studied in
literature to realize the late time acceleration. In this paper, we have chosen
a viable f(R) model and discussed its effects on the dynamical instability of
expansionfree fluid evolution generating a central vacuum cavity. For this
purpose, contracted Bianchi identities are obtained for both the usual matter
as well as dark source. The term dark source is named to the higher order
curvature corrections arising from f(R) gravity. The perturbation scheme is
applied and different terms belonging to Newtonian and post Newtonian regimes
are identified. It is found that instability range of expansionfree fluid on
external boundary as well as on internal vacuum cavity is independent of
adiabatic index $\Gamma$ but depends upon the density profile, pressure
anisotropy and f(R) model.
