This article is cited in 20 papers

On the polyvariance of the base equations of coupled micropolar thermoelasticity

E. V. Murashkin, Yu. N. Radayev

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow

Abstract: The paper is devoted to the study of dynamic equations polyvariance of the theory of semiisotropic micropolar thermoelasticity. Several variants for assigning integer weights to field variables with subsequent determination of algebraic weights of pseudo-vector equations for the dynamics of a semiisotropic thermoelastic solid are considered and analyzed. For this aim elementary volumes and areas assumed as pseudoinvariants of odd integer weights. In addition, it is shown that odd weights can be assigned to the pseudovector of spinor displacements. As a result, heat flux, force stress tensor, mass density, heat capacity, and shear modulus also can be treated as pseudotensor quantities of odd weights, i.e. manifest itself sensitivity to mirror reflections and inversions of three-dimensional spaces. The fundamental principle of absolute invariance of absolute thermodynamic temperature is discussed. Some variants of the coupled system of differential equations of dynamics and heat conduction equations for a semiisotropic micropolar thermoelastic solid are obtained. The problems of mutual influence of algebraic weights of constitutive pseudoscalars are discussed in order to taking account of their response to transformations of three-dimensional space that change its orientation to the opposite.

Keywords: polyvariance, nanoscale, microscale, nanostructural state, characteristic microlength, shear modulus of elasticity, thermal conductivity, micropolarity, tensor volume element, heat flux pseudovector, pseudotensor, specular reflection, semiisotropic solid, gyrotropic solid.

UDC: 539.374

Received: 20.09.2023
Accepted: 05.12.2023

DOI: 10.37972/chgpu.2023.57.3.010