Geodesic
Constitutive equations with dissipative stresses
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2023), pp. 47-55 
I. N. Molodtsov. Constitutive equations with dissipative stresses. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2023), pp. 47-55. http://geodesic.mathdoc.fr/item/VMUMM_2023_3_a7/
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     author = {I. N. Molodtsov},
     title = {Constitutive equations with dissipative stresses},
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     year = {2023},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new class of constitutive equations for complex loading processes is obtained. It has three state functionals. A new method of mathematical modeling and mathematical principle is formulated. According to them, physically correct equations of state are changed by including gyroscopic terms in them that do not perform mechanical work. The constitutive equations of complex loading processes with two state functionals under conditions of soft and hard loadings are constructed. Their connection with the Ilyushin formula and modern theories of plastic flow is obtained. A mathematical model of the domain mechanism of plasticity is formulated. It represents a real deformable continuum as a mixture of an elastoplastic continuum and a Cosserat continuum – flat veinlets (domain of plastic deformation – zones of large relative rotations). A physical justification for the inclusion of the asymmetric part of the stress and rotation tensor in the composition of the thermodynamic parameters of the model is given.

[1] Ilyushin A.A., “Funktsionaly i mery neobratimosti na mnozhestve protsessov v mekhanike sploshnoi sredy (MSS)”, Dokl. RAN, 337:1 (1994), 48–50

[2] Ilyushina G.A., “O resheniyakh termodinamicheskogo uravneniya dlya funktsionala reaktsii v prostranstve nepreryvno differentsiruemykh protsessov”, Vestn. Mosk. un-ta. Matem. Mekhan., 1996, no. 2, 75–79 | MR

[3] Ilyushin A.A., Plastichnost, Izd-vo AN SSSR, M., 1963

[4] Kunin I.A., Teoriya uprugikh sred s mikrostrukturoi, Nauka, M., 1975

[5] Ogibalov P.M., Tambovtsev E.P., Molodtsov I.N., “Nelokalnaya teoriya strukturirovannykh kompozitnykh materialov”, Mekhan. kompozit. materialov, 3 (1984), 408–416

[6] Ogibalov P.M., Tambovtsev E.P., Molodtsov I.N., “Dinamicheskaya kalibrovka dissipatsii v kompozitnykh nelokalnykh sredakh”, Mekhan. kompozit. materialov, 2 (1985), 17–24

[7] Molodtsov I.N., “Ochagovyi mekhanizm plastichnosti i dinamicheskaya kalibrovka uravnenii sostoyaniya”, Izv. TulGU. Ser. Matem. Mekhan. Inform., 6:2 (2000), 116–119