Geodesic
A nonlinear Maxwell-type model for rheonomous materials: stability under symmetric cyclic loadings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2018), pp. 59-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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The analytic study of the nonlinear Maxwell-type constitutive relation with two arbitrary material functions is continued to reveal its capabilities, applicability scope, and techniques of identification and tuning. General properties of the model response to an arbitrary periodic loading program are considered. A criteria for periodicity of strain evolution (and for the lack of ratcheting) is obtained. A condition is derived for simulation of cyclic stability under symmetric cyclic loadings, i.e., the effect of hysteresis loops stabilization after a number of cycles and convergence to a closed one. The condition is proved to depend only on a one material function and to be consistent with tension compression asymmetry simulation. 
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     author = {A. V. Khokhlov},
     title = {A nonlinear {Maxwell-type} model for rheonomous materials: stability under symmetric cyclic loadings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {59--63},
     year = {2018},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_2_a8/}
}
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A. V. Khokhlov. A nonlinear Maxwell-type model for rheonomous materials: stability under symmetric cyclic loadings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2018), pp. 59-63. http://geodesic.mathdoc.fr/item/VMUMM_2018_2_a8/

[1] Moskvitin V.V., Tsiklicheskoe nagruzhenie elementov konstruktsii, Nauka, M., 1981 | MR

[2] Makhutov N.A., Burak M.I., Gadenin M.M. i dr., Mekhanika malotsiklovogo razrusheniya, Nauka, M., 1986

[3] Kang G., “Ratchetting: recent progresses in phenomenon observation, constitutive modeling and application”, Int. J. Fatigue, 30 (2008), 1448–1472 | DOI

[4] Fuschi P., Pisano A.A., Weichert D., Direct Methods for Limit and Shakedown Analysis of Structures: Advanced Computational Algorithms and Material Modelling, Springer, Berlin, 2015

[5] Khokhlov A.V., “Svoistva nelineinoi modeli vyazkouprugoplastichnosti tipa Maksvella s dvumya materialnymi funktsiyami”, Vestn. Mosk. un-ta. Matem. Mekhan., 2016, no. 6, 36–41 | Zbl

[6] Khokhlov A.V., “Krivye dlitelnoi prochnosti nelineinoi modeli vyazkouprugoplastichnosti tipa Maksvella i pravilo summirovaniya povrezhdennosti pri stupenchatykh nagruzheniyakh”, Vestn. Samar. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2016, no. 3, 524–543 | DOI

[7] Khokhlov A.V., “Svoistva semeistva krivykh nagruzheniya s postoyannoi skorostyu, porozhdaemykh nelineinoi modelyu vyazkouprugoplastichnosti tipa Maksvella”, Mashinostroenie i inzhenernoe obrazovanie, 2017, no. 1, 57–71

[8] Khokhlov A.V., “Nelineinaya model vyazkouprugoplastichnosti tipa Maksvella: modelirovanie vliyaniya temperatury na krivye deformirovaniya, relaksatsii i polzuchesti”, Vestn. Samar. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:1 (2017), 160–179 | DOI

[9] Khokhlov A.V., “Nelineinaya model vyazkouprugoplastichnosti tipa Maksvella: skorost nakopleniya plasticheskoi deformatsii pri tsiklicheskikh nagruzheniyakh”, Deformatsiya i razrushenie materialov, 2017, no. 7, 7–19

[10] Khokhlov A.V., “Identifikatsiya nelineinoi modeli uprugovyazkoplastichnosti tipa Maksvella po krivym polzuchesti s nachalnoi stadiei nagruzheniya. Ch. 2. Metodiki”, Deformatsiya i razrushenie materialov, 2017, no. 10, 2–9

[11] Kang G., Ding J., Liu Y., “Summary on Uniaxial Ratchetting of 6061-T6 Aluminium Alloy”, Aluminium Alloys, Theory and Applications, 2011, 199–216, InTech | DOI

[12] Arutyunyan R.A., Kamentseva Z.P., “Uprochnenie stareyuschikh splavov”, Izv. AN SSSR. Mekhan. tverdogo tela, 1976, no. 4, 128–137

[13] Arutyunyan R.A., Vakulenko A.A., Umanskii S.E., “O tsiklicheskom nagruzhenii plasticheskoi sredy so stareniem”, Izv. AN SSSR. Mekhan. tverdogo tela, 1979, no. 2, 79–83 | MR