Nonlinearities in the nematic stress tensor

We derive quadratic nonlinearities in the viscoelastic stress tensor for nematic liquid crystals, which are necessary for the analysis of observed nonlinear effects in ultrasonic and electrohydrodynamic regimes. An increase in magnitude of the Leslie-Ericksen viscosity coefficients occurs through additive nonlinear terms as velocity gradients increase. The viscous components of the stress tensor are obtained for a nematic liquid crystal as a function of the velocity gradient components. Direct tests for determining the magnitude of single quadratically nonlinear viscosity coefficients are proposed.