Geodesic
Use of a one-parameter family of Gordon–Showalter objective derivatives to describe finite deformations of viscoelastic bodies
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2017), pp. 64-68 
E. D. Martynova; N. S. Stetsenko. Use of a one-parameter family of Gordon–Showalter objective derivatives to describe finite deformations of viscoelastic bodies. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2017), pp. 64-68. http://geodesic.mathdoc.fr/item/VMUMM_2017_6_a11/
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     author = {E. D. Martynova and N. S. Stetsenko},
     title = {Use of a one-parameter family of {Gordon{\textendash}Showalter} objective derivatives to describe finite deformations of viscoelastic bodies},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {64--68},
     year = {2017},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_6_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A constitutive relation is considered for viscoelastic materials under finite deformations. This relation is obtained using a one-parameter family of Gordon–Schowalter objective derivatives and generalizes the elementary Maxwell model. It is shown that, in the problem of simple shear of an incompressible viscoelastic material, this constitutive relation allows one to obtain the Poynting effect for any parameters of the model.

[1] Ilyushin A. A., Pobedrya B.E., Osnovy matematicheskoi teorii termovyazkouprugosti, Nauka, M., 1970 | MR

[2] Lure A.I., Nelineinaya teoriya uprugosti, Nauka, M., 1980 | MR

[3] Brovko G.L., “Nekotorye podkhody k postroeniyu opredelyayuschikh sootnoshenii plastichnosti pri bolshikh deformatsiyakh”, Uprugost i neuprugost, eds. M.Sh. Israilov, A.P. Shmakov, V.S. Lenskii, Izd-vo MGU, M., 1987, 68–81 | MR

[4] Oldroyd J.G., “On the formulation of rheological equations of states”, Proc. Roy. Soc. London, A 200 (1950), 523–541 | DOI | MR | Zbl

[5] Gordon J.R., Schowalter W.R., “Anisotropic fluid theory: a different approach to the dumbbell theory of dilute polymer solutions”, Trans. Soc. Rheol., 16 (1972), 79–97 | DOI | Zbl

[6] Brovko G.L., “Svoistva i integrirovanie nekotorykh proizvodnykh po vremeni ot tenzornykh protsessov v mekhanike sploshnoi sredy”, Izv. AN SSSR. Mekhan. tverdogo tela, 1990, no. 1, 54–60 | MR

[7] Trusdell K., Pervonachalnyi kurs ratsionalnoi mekhaniki sploshnykh sred, Mir, M., 1975