  We consider a collapsing sphere and discuss its evolution under the vanishing
expansion scalar in the framework of $f(R)$ gravity. The fluid is assumed to be
locally anisotropic which evolves adiabatically. To study the dynamics of the
collapsing fluid, Newtonian and post Newtonian regimes are taken into account.
The field equations are investigated for a well-known $f(R)$ model of the form
$R+\delta R^2$ admitting Schwarzschild solution. The perturbation scheme is
used on the dynamical equations to explore the instability conditions of
expansionfree fluid evolution. We conclude that instability conditions depend
upon pressure anisotropy, energy density and some constraints arising from this
theory.
