Abstract:
The paper is devoted to problems concerning the tensors with constant components, hemitropic tensors and pseudotensors that are of interest from the point of view of micropolar continuum mechanics. The properties and coordinate representations of tensors and pseudotensors with constant components are discussed. Based on an unconventional definition of a hemitropic fourth-rank tensor, a coordinate representations in terms of Kronecker deltas and metric tensors are given. A comparison of an arbitrary hemitropic fourth-rank tensor and a tensor with constant components are discussed. The coordinate representations for constitutive tensors and pseudotensors used in mathematical modeling of linear hemitropic micropolar continuums are given in terms of the metric tensor.The covariant constancy of fourth-rank pseudotensors with constant components and hemitropic tensors is considered and discussed.
The work was carried out within the framework of a state assignment (state registration no. AAAA–A20–120011690132–4) and with the support of the Russian Foundation for Basic Research (project no. 20–01–00666).
Citation:
E. V. Murashkin, Yu. N. Radayev, “On the theory of fourth-rank hemitropic tensors in three-dimensional Euclidean spaces”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:3 (2022), 592–602
\Bibitem{MurRad22}
\by E.~V.~Murashkin, Yu.~N.~Radayev
\paper On the theory of fourth-rank hemitropic tensors in three-dimensional Euclidean spaces
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2022
\vol 26
\issue 3
\pages 592--602
\mathnet{http://mi.mathnet.ru/vsgtu1941}
\crossref{https://doi.org/10.14498/vsgtu1941}
\edn{https://elibrary.ru/AFCREX}
Linking options:
https://www.mathnet.ru/eng/vsgtu1941
https://www.mathnet.ru/eng/vsgtu/v226/i3/p592
This publication is cited in the following 4 articles:
T.K. Nesterov, “Plane harmonic waves in a hemitropic micropolar body”, Vestnik Chuvashskogo gosudarstvennogo pedagogicheskogo universiteta im. I.Ya. Yakovleva. Seriya: Mekhanika predelnogo sostoyaniya, 2024, no. 1(59), 115
Yu. N. Radaev, “TENZORY S POSTOYaNNYMI KOMPONENTAMI V OPREDELYaYuSchIKh URAVNENIYaKh GEMITROPNOGO MIKROPOLYaRNOGO TELA”, Izvestiya Rossiiskoi akademii nauk. Mekhanika tverdogo tela, 2023, no. 5, 98
E. V. Murashkin, Y. N. Radayev, “A Negative Weight Pseudotensor Formulation of Coupled Hemitropic Thermoelasticity”, Lobachevskii J Math, 44:6 (2023), 2440
Y. N. Radayev, “Tensors with Constant Components in the Constitutive Equations of a Hemitropic Micropolar Solids”, Mech. Solids, 58:5 (2023), 1517
Citation in format AMSBIB
Contact us: