Interrelation of Heat Propagation and Angular Velocity in Micropolar Media

Abstract

This paper is concerned with a materials model within the framework of an extended theory of micropolar media. The extension affects the balance for the tensor field of micro-inertia which, in contrast to the common theory, will now contain a production term. As a consequence the tensor of the moment of inertia becomes an independent field varying in space and time and obeys its own partial differential equation: an extended balance of micro-inertia. The production becomes important if the micropolar material undergoes structural changes. In the present case we consider on the mesoscale an assemblage of statistically uniformly distributed particles of arbitrary shape, which we treat macroscopically as an isotropic linear-thermoelastic continuum. The structural change is then due to a space-dependent transient increase of the temperature field, which leads to an inhomogeneous time-varying expansion of an equivalent thermo-elastic medium. On the continuum scale this will lead to a changing moment of inertia field. For this situation a possible form of the production term on the continuum level can be motivated from mesoscopic considerations and then be evaluated numerically together with the extended balance of micro-inertia. In addition, the temporal and spatial change of the macroscopic inertia field influences rotational motion. By solving the balance of spin numerically the angular velocity evolving in space and time will be determined. The impact of viscosity in the expression of the couple stress will be investigated and different choices of boundary conditions will be proposed when solving the coupled thermo-mechanical problem.