Continuum Mechanics for Higher-Stage Micropolar Materials (4th Report, Discussions of Thermodynamics for Constitutive Equations)

Constitutive equations for higher-stage micropolar materials must be discussed thermodynamically as a preliminary to the construction of concrete constitutive equations. In the present paper averaging the 1st and 2nd laws of thermodynamics is the microscopic volume elements up to stage-2, the energy balance equation and the entropy inequality for the micropolar materials of stage-2 are formulated on the basis of the results of the previous reports. Thermodynamic relationships between the generalized forces (stress, couple stress, bicouple stress, heat flux density) and thermodynamic functions (free energy and dissipation function) which govern the constitutive equations are derived using the Clausius-Duhem inequality obtained by coupling the energy balance equation and entropy inequality. In this way, the thermodynamic limitations which the constitutive equations must satisfy are clarified, and the response functions and their arguments which characterize the constitutive equations are determined.