{"title":"Theory of Poisson’s Ratio for a Thermoelastic Micropolar Acentric Isotropic Solid","authors":"E. V. Murashkin, Y. N. Radayev","doi":"10.1134/s1995080224602480","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The present paper deals with the triple weights pseudotensor formulation of multivariant thermoelasticity for acentric isotropic micropolar solids. The fundamental concepts of pseudoinvariant volume/area/arc elements of odd integer weights in three-dimensional spaces are discussed. The developed theory of acentric isotropic micropolar thermoelasticity is formulated in terms of contravariant pseudovector of spinor displacements having positive odd algebraic weight and covariant absolute vector of translational displacements. Three energetic forms (H), (E), and (A) of thermoelasticity potential are proposed. The latter is derived from the irreducible system of algebraic invarinats/pseudoinvariants being actually their linear span with coefficients thus allowing us to introduce the conventional thermoelasticity moduli (shear modulus of elasticity, Poisson’s ratio, characteristic nano/microlength, etc.). For others energetic forms thermoelasticity anisotropic micropolar (E) moduli are determined via (A) moduli and then (H) moduli are found in terms of (A) moduli. The triple weights formulation of multivariant constitutive equations for acentric isotropic thermoelastic solid are obtained and analyzed. A comparison of proposed multivariant constitutive equations elucidates the absolute invariance of Poisson’s ratio, i.e., it insensibility to mirror reflections and prohibition of assigning any algebraic weight to this constitutive scalar.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602480","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The present paper deals with the triple weights pseudotensor formulation of multivariant thermoelasticity for acentric isotropic micropolar solids. The fundamental concepts of pseudoinvariant volume/area/arc elements of odd integer weights in three-dimensional spaces are discussed. The developed theory of acentric isotropic micropolar thermoelasticity is formulated in terms of contravariant pseudovector of spinor displacements having positive odd algebraic weight and covariant absolute vector of translational displacements. Three energetic forms (H), (E), and (A) of thermoelasticity potential are proposed. The latter is derived from the irreducible system of algebraic invarinats/pseudoinvariants being actually their linear span with coefficients thus allowing us to introduce the conventional thermoelasticity moduli (shear modulus of elasticity, Poisson’s ratio, characteristic nano/microlength, etc.). For others energetic forms thermoelasticity anisotropic micropolar (E) moduli are determined via (A) moduli and then (H) moduli are found in terms of (A) moduli. The triple weights formulation of multivariant constitutive equations for acentric isotropic thermoelastic solid are obtained and analyzed. A comparison of proposed multivariant constitutive equations elucidates the absolute invariance of Poisson’s ratio, i.e., it insensibility to mirror reflections and prohibition of assigning any algebraic weight to this constitutive scalar.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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