  We perform statistical mechanics calculations to analyze the global phase
diagram of a fully-connected version of a Maier-Saupe-Zwanzig lattice model
with the inclusion of couplings to an elastic strain field. We point out the
presence of uniaxial and biaxial nematic structures, depending on temperature
$T$ and on the applied stress $\sigma$. Under uniaxial extensive tension,
applied stress favors uniaxial orientation, and we obtain a first-order
boundary, along which there is a coexistence of two uniaxial paranematic
phases, and which ends at a simple critical point. Under uniaxial compressive
tension, stress favors biaxial orientation; for small values of the coupling
parameters, the first-order boundary ends at a tricritical point, beyond which
there is a continuous transition between a paranematic and a biaxially ordered
structure. For some representative choices of the model parameters, we obtain a
number of analytic results, including the location of critical and tricritical
points and the line of stability of the biaxial phase.
