Martynova, E. D. Lagrangian representation of the family of Gordon-Schowalter objective derivatives at simple shear. (English. Russian original) Zbl 1472.74009 Mosc. Univ. Mech. Bull. 75, No. 6, 176-179 (2020); translation from Vestn. Mosk. Univ., Ser. I 75, No. 6, 63-66 (2020). Summary: The paper deals with the one-parameter family of Gordon-Schowalter objective derivatives including the Oldroyd, Cotter-Rivlin, and Jaumann derivatives. For a simple shear, movable bases are found in which the considered differential operators are reduced to the total time derivatives of the tensor components. For all derivatives of the family under consideration, except for Oldroyd and Cotter-Rivlin derivatives, the basis vectors lying in the shear plane rotate with a certain period changing their length and mutual orientation. MSC: 74A20 Theory of constitutive functions in solid mechanics 74A05 Kinematics of deformation 74D10 Nonlinear constitutive equations for materials with memory Keywords:finite deformation; one-parameter family; moving basis; Oldroyd derivative; Cotter-Rivlin derivative; viscoelasticity × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Truesdell, C., A First Course in Rational Continuum Mechanics (1972), Baltimore, MD: The Johns Hopkins Univ., Baltimore, MD [2] Brovko, G. L., Constitutive Relations of Continuum Mechanics. Development of the Mathematical Apparatus and Fundamentals in the General Theory (2017), Moscow: Nauka, Moscow [3] Gordon, R. J.; Schowalter, W. R., Anisotropic fluid theory: a different approach to the dumbbell theory of dilute polymer solutions, Trans. Soc. Rheol., 16, 79-97 (1972) · Zbl 0368.76006 · doi:10.1122/1.549256 [4] Brovko, G. L., “Properties and integration of some time derivatives of tensor processes in continuum mechanics,” Izv. Akad. Nauk SSSR. Mekh. Tverd, Tela, No., 2, 54-60 (1990) [5] Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T., Modern Geometry. Methods and Applications (1986), Moscow: Nauka, Moscow · Zbl 0601.53001 [6] Martynova, E. D.; Stetsenko, N. S., Use of a one-parameter family of Gordon-Schowalter objective derivatives to describe finite strains of viscoelastic bodies, Moscow Univ. Mech. Bull., 72, 153-156 (2017) · Zbl 1394.74031 · doi:10.3103/S002713301706005X 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.