Geodesic
General resulting forms of constitutive relations in the classical continuum mechanics
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2018), pp. 67-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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The theory of constitutive relations of deformation resistance of bodies is constructed provided simultaneously by possible presence of inner kinematic constraints in a body and by account of internal body forces. The axioms of the theory are proposed and the general reduced form of the system of constitutive relations is derived. For simple bodies (classical media), the equivalence of Ilyushin's and Noll's forms of constitutive relations is established. 
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G. L. Brovko. General resulting forms of constitutive relations in the classical continuum mechanics. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2018), pp. 67-71. http://geodesic.mathdoc.fr/item/VMUMM_2018_2_a10/

[1] Ilyushin A.A., Mekhanika sploshnoi sredy, Izd-vo Mosk. un-ta, M., 1990

[2] Sedov L.I., Mekhanika sploshnoi sredy, v. 1, 2, Nauka, M., 1984 | MR

[3] P. S. Aleksandrov (red.), Problemy Gilberta, Nauka, M., 1969

[4] Noll W., “A mathematical theory of the mechanical behavior of continuous media”, Arch. Ration. Mech. and Anal., 2 (1958), 197–226 | DOI | MR | Zbl

[5] Truesdell C., Noll W., The non-linear field theories of mechanics, Handbuch der Physik, III/3, Springer-Verlag, Berlin, 1965 ; 3rd ed., ed. Stuart S. Antman, Springer-Verlag, Berlin–Heidelberg–N.Y. et al., 2004 | MR | Zbl

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

[7] Gurtin M. E., Fried E., Anand L., The mechanics and thermodynamics of continua, Cambridge University Press, Cambridge–N.Y. et al., 2010 | MR

[8] Brovko G.L., Osnovy mekhaniki sploshnoi sredy (kratkii konspekt lektsii, zadachi, uprazhneniya), v. 2, Popechit. sovet mekh.-mat. f-ta MGU im. M.V. Lomonosova, M., 2013

[9] Brovko G.L., “Ponyatiya obraza protsessa i pyatimernoi izotropii svoistv materialov pri konechnykh deformatsiyakh”, Dokl. AN SSSR, 308:3 (1989), 565–570 | MR | Zbl

[10] Brovko G.L., “Materialnye i prostranstvennye predstavleniya opredelyayuschikh sootnoshenii deformiruemykh sred”, Prikl. matem. i mekhan., 54:5 (1990), 814–824 | MR | Zbl

[11] Brovko G.L., Razvitie matematicheskogo apparata i osnov obschei teorii opredelyayuschikh sootnoshenii mekhaniki sploshnoi sredy, Dokt. dis., M., 1996

[12] Brovko G.L., Ivanova O.A., Finoshkina A.S., “On geometrical and analytical aspects in formulations of problems of classic and non-classic continuum mechanics”, Operator Theory: Advances and Applications, 191, Birkhäuser-Verlag, Basel/Switzerland, 2009, 51–79 | MR | Zbl

[13] Brovko G.L., “On general principles of the theory of constitutive relations in classical continuum mechanics”, J. Eng. Math. Kluwer Acad. Publ., 78 (2013), 37–53 | DOI | MR | Zbl