On Thermodynamically Consistent Form of Nonlinear Equations of the Cosserat Theory

To describe motion in a micropolar medium a special measure of curvature is used that is a strain state characteristic independent of deformation process. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against three independent coefficients of the classical theory. So, it turns out that the developed variant of the model gives an adequate description of generalized plane stress state in an isotropic micropolar medium, while the classical one describes this state only at a certain case. The complete system of nonlinear equations for the dynamics of a medium with couple stresses reduces to a thermodynamically consistent system of laws of conservation, which allows obtaining integral estimates that guarantee the correctness of the Cauchy problem and boundary-value problems with dissipative boundary conditions.