Two-Sided Estimates for the Relaxation Function of the Linear Theory of Heredity via the Relaxation Curves during the Ramp-Deformation and the Methodology of Identification

The general properties of the relaxation curves with the initial stage of deformation and their dependence on the duration of the initial stage of deformation and the properties of the relaxation function are analytically studied. These curves are induced by the constitutive equation of viscoelasticity with an arbitrary relaxation. New accurate two-sided estimates for the relaxation curves and their absolute and relative deviations from the relaxation curves for instantaneous deformation are derived. The uniform convergence of the set of relaxation curves when the duration of the initial stage tends to zero is proved.