This article is cited in 17 papers

Multiweights thermomechanics of hemitropic micropolar solids

E. V. Murashkin^a, Yu. N. Radayev

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

Abstract: The article is devoted to the problems of determining the algebraic weights of microand nanoscale multi-weight characteristics of the hemitropic micropolar thermomechanics. The fundamental concepts of pseudoinvariant volume and area elements of odd integer weights in threedimensional space are discussed. The developing theory of hemitropic micropolar thermoelasticity is formulated in terms of a contravariant pseudovector of spinor displacements of a positive odd weight with the fundamental principle of the absolute invariance of absolute thermodynamic temperature, mass and mass densities of: entropy, internal energy, Helmholtz free energy, controlled and uncontrolled entropy production. Multi-weight pseudotensor formulations of wireless transmission principles and a reduced energy balance equation are proposed. Multiweights formulas for pseudovector differential equations of statics and dynamics of a hemitropic thermoelastic body are obtained and analyzed. The problem of mutual influence of algebraic weights of constitutive pseudoscalars are discussed in order to take into account their transformations as a result of the transformation of three-dimensional space, changing the orientation of the coordinate basis to the opposite.

Keywords: algebraic weight, pseudotensor, nanoscale, microscale, heat conduction, micropolarity, tensor volume element, multiweight formulation, heat flux pseudovector, mirror reflection, hemitropic solid.

UDC: 539.374

Received: 20.09.2023
Accepted: 20.12.2022

DOI: 10.37972/chgpu.2023.58.4.010