Constraints,dissipation functions and cholesteric liquid crystals

Our recently introduced dissipation function theory of molecular liquids and solids is extended to include constrained motions. Lagrangian multipliers are used in the reversible parts of the field equations of motion. Conservation laws of mass, momentum, energy and angular momentum are derived (in both the material and spatial frames) and shown to hold under the same general conditions as in the unconstrained case. Our theory is then applied to liquid crystals. Within our formalism, constitutive relations characterizing linear and nonlinear liquid crystals are given. In the linear regime, for cholesterics, depending on whether the heat flux or the temperature gradient is used in the dissipation function we show that different reciprocal relations follow. Our results for incompressible nematics and cholesterics are compared with the Ericksen-Leslie theory and others.