Tensors with constant components in the constitutive equations of a hemitropic micropolar solids. (English. Russian original) Zbl 07792090
Mech. Solids 58, No. 5, 1517-1527 (2023); translation from Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela 2023, No. 5, 98-110 (2023).
MSC:
| 74A35 | Polar materials |
| 74A20 | Theory of constitutive functions in solid mechanics |
| 15A72 | Vector and tensor algebra, theory of invariants |
Keywords:
quadratic stress potential; semi-anisotropic solid; contravariant translational displacement field; contravariant pseudovector microrotation field; constitutive pseudo-tensorReferences:
| [1] | L. A. Pars, A Treatise on Analytical Dynamics (Heinemann, London, 1965; Nauka, Moscow, 1971). · Zbl 0125.12004 |
| [2] | Cosserat, E.; Cosserat, F., Théorie des Corps Déformables (1909), Paris: Herman et Fils, Paris · JFM 40.0862.02 |
| [3] | Nowacki, W., Theory of Asymmetric Elasticity (1986), Oxford: Pergamon Press, Oxford · Zbl 0604.73020 |
| [4] | G. B. Gurevich, Foundations of the Theory of Algebraic Invariants (GITTL, Moscow, Leningrad, 1948; Groningen, Noordhoff, 1964). |
| [5] | Radayev, Y. N., “The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories,” Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-, Mat. Nauki, 22, 504-517 (2018) · Zbl 1424.74008 · doi:10.14498/vsgtu1635 |
| [6] | Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N., “On the Neuber theory of micropolarelasticity. A pseudotensor formulation,” Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-, Mat. Nauki, 24, 752-761 (2020) · Zbl 1463.74019 · doi:10.14498/vsgtu1799 |
| [7] | Murashkin, E. V.; Radayev, Y. N., An algebraic algorithm of pseudotensors weights eliminating and recovering, Mech. Solids, 57, 1416-1423 (2022) · doi:10.3103/s0025654422060085 |
| [8] | Murashkin, E. V.; Radayev, Y. N., On theory of oriented tensor elements of area for a micropolar continuum immersed in an external plane space, Mech. Solids, 57, 205-213 (2022) · Zbl 1519.74001 · doi:10.3103/s0025654422020108 |
| [9] | Murashkin, E. V.; Radayev, Y. N., “On the theory of fourth-rank hemitropic tensors in three-dimensional Euclidean spaces,” Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-, Mat. Nauki, 26, 592-602 (2022) · Zbl 1513.15047 · doi:10.14498/vsgtu1941 |
| [10] | E. V. Murashkin and Yu. N. Radayev, “On two base natural forms of asymmetric force and couple stress tensors of potential in mechanics of hemitropic solids,” Vestn. Chuvash. Gos. Ped. Univ. Im. I. Ya. Yakovleva Ser.: Mekh. Pred. Sost., No. 3 (53), 86-100 (2022). doi:10.37972/chgpu.2022.53.3.010 |
| [11] | Jeffreys, H., Cartesian Tensors (1969), Cambridge: Cambridge Univ. Press, Cambridge |
| [12] | Y. N. Radayev, “Two-point rotations in geometry of finite deformations,” in Theory of Elasticity and Creep. Advanced Structured Materials, Vol. 185 (Springer, 2023), pp. 275-283. doi:10.1007/978-3-031-18564-9_20 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
