Derivation of Theory of Thermoviscoelasticity by Means of Two-component Cosserat Continuum

Abstract

We consider a mechanical model of a two-component medium whose first component is the classical continuum and the other component is the continuum having only rotational degrees of freedom. We show that the proposed model can be used for description of thermal and dissipative phenomena. Interpretation of the temperature, entropy and other thermodynamic quantities given in accordance with the proposed model is no more than the mechanical analogy. However, use of these mechanical counterparts allows one to obtain the well-known equations describing the thermal and diffusion processes within the framework of the model. The mathematical description of the proposed mechanical model includes as special cases not only the classical formulation of coupled problem of thermoelasticity but also the formulation of the coupled problem of thermoelasticity with the hyperbolic type heat conduction equation. In the context of the proposed mechanical model, an original interpretation of the volume (acoustic) viscosity and the shear viscosity is offered.