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

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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. 
@article{VMUMM_2018_2_a8,
     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},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     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/