Effect of the Initial Stage of Strain on the Properties of Relaxation Curves Generated by the Rabotnov Nonlinear Relation for Viscoelastic Materialsстатья
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Аннотация:Khokhlov A.V. Influence of initial stage of deformation on the properties of stress relaxation curves produced by the Rabotnov non-linear relation for viscoelastic materials.
*** Хохлов А.В. Оценка влияния начальной стадии деформирования на свойства кривых релаксации, порождаемых нелинейным соотношением Работнова для вязкоупругих материалов // Вестник Московского университета. Сер. 1: Математика. Механика. 2019. № 4. С. 28-33. ***
The general equation of stress relaxation curves family generated by the Rabotnov nonlinear constitutive equation (with two arbitrary material functions) under arbitrary non-decreasing strain histories at initial stage of deformation up to a given strain level is derived and studied analytically. Influence of the initial stage shape and rise time influence on the properties of the theoretic relaxation curves are examined. Effective general bounds have been 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, convergence of the relaxation curves family (with fixed strain level and initial stage shape) to the relaxation curve under step loading has been proved.
*** Keywords: elastoviscoplasticity, physical non-linearity, stress relaxation curves, ramp tests, rise time influence, influence of initial stage of deformation, bounds for ramp relaxation curves, asymptotics, convergence, fading memory, applicability indicators, identification