On Algebraic Triple Weights Formulation of Micropolar Thermoelasticity

• Published in: Mechanics of solids Vol. 59; no. 1; pp. 555 - 580
• Main Authors: Murashkin, E. V., Radayev, Y. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.02.2024; Springer Nature B.V
• Subjects: Classical Mechanics; Controllability; Differential equations; Entropy; Free energy; Internal energy; Modulus of elasticity; Physics; Physics and Astronomy; Principles; Shear modulus; Thermodynamics; Thermoelasticity; nanoscale; micropolarity; pseudotensor; heat conduction; heat flux pseudovector; nano/micro length; triple weights formulation; algebraic weight; microscale; hemitropic solid; tensor volume element; mirror reflection
• ISSN: 0025-6544; 1934-7936
• DOI: 10.1134/S0025654424700274

In the present paper triple formulation of the thermomechanics of hemitropic micropolar solids are proposed and then reduced to the three positive, negative and zero weights variants. The fundamental concepts of pseudoinvariant volume and area elements of odd integer weights in three-dimensional space are discussed. The developed theory of hemitropic micropolar thermoelasticity is formulated in terms of a contravariant pseudovector of a positive odd weight representing spinor displacements, subject to the principle of absolute invariance of absolute thermodynamic temperature, mass and specific entropy, specific internal energy, specific Helmholtz free energy, specific controllable and uncontrollable entropy production. triple weights pseudotensor formulations of the principle of virtual displacements and the reduced energy balance equation are discussed. Corresponding differential equations of statics and dynamics of a hemitropic thermoelastic solid are obtained and analyzed. The sensibility of shear modulus of elasticity and characteristic microlength to re-orientations of three-dimensional space are revisited.