  We study a class of shear-free, homogeneous but anisotropic cosmological
models with imperfect matter sources in the context of f(R) gravity. We show
that the anisotropic stresses are related to the electric part of the Weyl
tensor in such a way that they balance each other. We also show that within the
class of orthogonal f(R) models, small perturbations of shear are damped, and
that the electric part of the Weyl tensor and the anisotropic stress tensor
decay with the expansion as well as the heat flux of the curvature fluid.
Specializing in locally rotationally symmetric spacetimes in orthonormal
frames, we examine the late-time behaviour of the de Sitter universe in $f(R)$
gravity. For the Starobinsky model of f(R), we study the evolutionary behavior
of the Universe by numerically integrating the Friedmann equation, where the
initial conditions for the expansion, acceleration and jerk parameters are
taken from observational data.
