  We construct and analyze a model for a disordered linear spring network with
anisotropy. The modeling is motivated by, for example, granular systems,
nematic elastomers, and ultimately cytoskeletal networks exhibiting some
underlying anisotropy. The model consists of a triangular lattice with two
different bond occupation probabilities, $p_x$ and $p_y$, for the linear
springs. We develop an effective medium theory (EMT) to describe the network
elasticity as a function of $p_x$ and $p_y$. We find that the onset of rigidity
in the EMT agrees with Maxwell constraint counting. We also find beyond linear
behavior in the shear and bulk modulus as a function of occupation probability
in the rigid phase for small strains, which differs from the isotropic case. We
compare our EMT with numerical simulations to find rather good agreement.
Finally, we discuss the implications of extending the reach of effective medium
theory as well as draw connections with prior work on both anisotropic and
isotropic spring networks.
