Type-II Thermoelasticity of Linear Anisotropic Micropolar Media

Abstract

In this paper, the mechanics of micropolar elastic solids is extended to a more general thermoelastic media in order to take account of the effect of temperature on their states and mechanical behavior. Since a thermoelastic micropolar medium conducts heat, it is required to include one or another mechanism of thermal propagation in the basic equations of micropolar thermoelasticity. A model of thermoelastic micropolar medium CGNII is developed on ground of the wave principle of heat transfer (i.e., thermal conductivity of the second type known from previous discussions by Green and Naghdi), characterized by zero internal entropy production. All the basic equations of the theory presented in this study are derived from the conventional balance equations of continuum mechanics and the fundamental thermodynamic inequality. Constitutive equations for a linear anisotropic thermoelastic micropolar medium (CGNII) are obtained by using a quadratic energy form for the Helmholtz free energy. Special attention is paid to hemitropic micropolar medium, when the components of one of the fourth rank constitutive pseudotensors demonstrate sensitivity to mirror reflections of three-dimensional space. A closed system of coupled differential equations is given in terms of translational displacement vector, spinor displacement vector and thermal displacement. It is important since can be used in formulations of applied problems of thermomechanics related to the wave heat transfer mechanism in micropolar elastic media.