Geodesic
Effect of the initial stage of strain on the properties of relaxation curves generated by the Rabotnov nonlinear relation for viscoelastic materials
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 28-33

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The general equation of stress relaxation curves family generated by the Rabotnov nonlinear constitutive equation (with two arbitrary material functions) under arbitrary strain histories at initial stage of deformation up to a given strain level is derived and studied analytically. The effect of the initial stage duration and shape on the properties of the relaxation curves is examined. Effective general bounds are obtained for differences of relaxation curves with different initial programs of deformation up to a given level and for their deviation from the relaxation curve under step loading via material functions and initial programs norms. As the rise time tends to zero, the convergence of the relaxation curves family (with a fixed strain level and initial stage shape) to the relaxation curve under step loading is proved. 
@article{VMUMM_2019_4_a3,
     author = {A. V. Khokhlov},
     title = {Effect of the initial stage of strain on the properties  of relaxation curves generated by the {Rabotnov} nonlinear relation for viscoelastic materials},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {28--33},
     publisher = {mathdoc},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a3/}
}
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A. V. Khokhlov. Effect of the initial stage of strain on the properties  of relaxation curves generated by the Rabotnov nonlinear relation for viscoelastic materials. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 28-33. http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a3/