  Analytical and numerical calculations are presented for the mechanical
response of fiber networks in a state of axisymmetric prestress, in the limit
where geometric non-linearities such as fiber rotation are negligible. This
allows us to focus on the anisotropy deriving purely from the non-linear
force-extension curves of individual fibers. The number of independent elastic
coefficients for isotropic, axisymmetric and fully anisotropic networks are
enumerated, before deriving expressions for the response to a locally applied
force that can be tested against e.g. microrheology experiments. Localised
forces can generate anisotropy away from the point of application, so numerical
integration of non-linear continuum equations is employed to determine the
stress field, and induced mechanical anisotropy, at points located directly
behind and in front of a force monopole. Results are presented for the wormlike
chain model in normalised forms, allowing them to be easily mapped to a range
of systems. Finally, the relevance of these findings to naturally occurring
systems and directions for future investigation are discussed.
