Abstract.A new method based on variable transformation is proposed for the estimation of the constant strain rate tensile test by using a previously introduced concept of viscoelastic response given to the real relaxation stimulus. The time range of the 'good' fitting is 2.5 to 3 times larger than the best results achieved using linear viscoelastic approximations. The theoretical background of the method was elucidated as well.

The relationship between the results of the tensile and the stress relaxation tests of polypropylene specimens were analyzed and an attempt was made to find a way to estimate the former from the latter based on the measurements and the theory of linear viscoelasticity. The mechanical response of real polymers are basically of nonlinear character, therefore their behavior patterns do not meet the idealized (linear) ones. Experiments were performed on poly(propylene) (PP) as a test material and the stress relaxation behavior, as well as the linear elastic and linear viscoelastic approximation of the tensile load‐time curve were analyzed. To demonstrate the applicability of our idea and to perform the numerical calculations we have chosen a flexible function with three parameters to realize the nonlinear behavior.

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The Reynolds–Orr equation predicts the unconditional stability limit of a flow. Although this seems to be a desirable aim in engineering applications, the predicted critical Reynolds numbers are one magnitude below the experimental observations. In this paper, an attempt is made to reduce this gap for incompressible shear flows. It is known that the Navier–Stokes equation has no regular solution at the initial time if the initial velocity field does not fulfill the compatibility condition. However, the original solution of the Reynolds–Orr equation, the critical perturbation, does not necessarily fulfill this condition. Therefore, the condition is added to the original problem as a non-linear constraint. This requires the use of a discrete functional, introduced in the paper. Two different formulations are implemented and discussed. The solution is assumed in a waveform. The augmented problem is solved in the cases of planar Poiseuille and the Couette flow. The result shows that adding the constraint increases the critical Reynolds number significantly in the case of a streamwise perturbation but only slightly in the case of a spanwise one. It was demonstrated using numerical simulations that the single waveform assumption was unreasonably strict. The usage of the compatibility condition without assuming the single waveform has a negligible effect on the critical Reynolds number. However, the presented methods can be used for adding other reasonable and complicated constraints to the variational problem.