Thermomechanical states of gyrotropic micropolar solids

E. V. Murashkin ; Yu. N. Radayev

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 4, pp. 659-678

Résumé

The paper is devoted to problems of modeling heat conduction processes in micropolar elastic solids, all thermomechanical states of which may be sensible to mirror reflections of three-dimensional space. A new variant of the heat conduction theory is developed in terms of the heat fluxes treated as pseudovectors of algebraic weight \(+1\) making their similar to the pseudovector of spinor displacements known from previous discussions. Constitutive pseudoinvariants (at least some of them) have odd negative weights (for example, thermal conductivity coefficient and specific heat). Having choosing elements of volume and area as natural known from the classical field theory formulations and considered as pseudoinvariants of weight \(-1\), the variant of theory is proposed. An absolute contravariant vector represents translational displacements and a contravariant pseudovector of weight \(+1\) does spinor displacements. As a result, heat flux, force stress tensor, mass density and specific heat can be treated as pseudotensor quantities of odd weights. The Helmholtz free energy per unit natural volume element is used as the thermodynamic potential with the functional arguments: temperature, symmetrical parts and accompanying vectors of the linear asymmetric strain tensor and wryness pseudotensor. The principle of absolute invariance of absolute thermodynamic temperature is proposed and discussed. A nonlinear heat conduction equation is obtained and linearized.

Détail

Keywords: heat conductivity, micropolarity, pseudovector of heat flux, mirror reflection, semiisotropic solid, gyrotropic solid, absolute thermodynamic temperature, weights balance rule
Mots-clés : tensor volume element, pseudotensor