  We use density functional plus $U$ methods to study the effects of a tensile
or compressive substrate strain on the charge-ordered insulating phase of
LuNiO$_3$. The numerical results are analyzed in terms of a Landau energy
function, with octahedral rotational distortions of the perovskite structure
included as a perturbation. Approximately 4% tensile or compressive strain
leads to a first-order transition from an insulating structure with large
amplitude breathing mode distortions of the NiO$_6$ octahedra to a metallic
state in which breathing mode distortions are absent but Jahn-Teller
distortions in which two Ni-O bonds become long and the other four become short
are present. Compressive strain produces uniform Jahn-Teller order with the
long axis aligned perpendicular to the substrate plane while tensile strain
produces a staggered Jahn-Teller order in which the long bond lies in the plane
and alternates between two nearly orthogonal in-plane directions forming a
checkerboard pattern. In the absence of the breathing mode distortions and
octahedral rotations, the tensile strain-induced transition to the staggered
Jahn-Teller state would be of second order.
