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We use density functional plus $U$ methods to study the effects of a tensileor compressive substrate strain on the charge-ordered insulating phase ofLuNiO$_3$. The numerical results are analyzed in terms of a Landau energyfunction, with octahedral rotational distortions of the perovskite structureincluded as a perturbation. Approximately 4% tensile or compressive strainleads to a first-order transition from an insulating structure with largeamplitude breathing mode distortions of the NiO$_6$ octahedra to a metallicstate in which breathing mode distortions are absent but Jahn-Tellerdistortions in which two Ni-O bonds become long and the other four become shortare present. Compressive strain produces uniform Jahn-Teller order with thelong axis aligned perpendicular to the substrate plane while tensile strainproduces a staggered Jahn-Teller order in which the long bond lies in the planeand alternates between two nearly orthogonal in-plane directions forming acheckerboard pattern. In the absence of the breathing mode distortions andoctahedral rotations, the tensile strain-induced transition to the staggeredJahn-Teller state would be of second order.

Strain Control of Electronic Phase in Rare Earth Nickelates