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RESUME For the description of shape memory alloys rheonomic properties the analogue of visco-plastic model with power parameter n has been introduced.

The proposal to apply this parameter is driven by the evident nonlinearity of the experimental curve shape after the stress jump in the process of stress-controlled stepwise load.

That was the principle reason of weak agreement between the experimental data and the model curves, produced by the linear models, which had been introduced earlier.

It has been proved that for any process, which might be conceptually split into subprocesses, either of which is an active monotonic stress process or an nonactive stress process in any internal point, upon condition of and both n and (which is Weibull’s function power parameter) are integers, the necessary and sufficient condition for disregarding the positive value execution function (hereinafter is referred to as angular brackets) from the model principal equations is the following: the difference between limiting slow and limiting fast process strain should be nonnegative and nondecreasing function of stress.

The method of model calibration, which implies a least squares approach and is based on the experimental data from the process of stress-controlled stepwise load, has been proposed.

By means of this method the independent parameters estimation was performed for the models with n=1 and n=3.

For all sets of retrieved parameters the condition for angular brackets removal jointly with the final stress non-negativity condition for the process of stress relaxation were verified.

It was detected that the model curves with n=3 and experimental data are coincide much tighter (in comparison to the model curves, constructed by the model without power parameter, which is equivalent to the n=1 model) for the stress-controlled stepwise load process.

The simulation results in terms of dimensional variables using the calibrated models for n=1 and n=3 for the monotone stress-controlled and strain-controlled load processes, stress relaxation process and stress-controlled stepwise load process were presented.

For the processes of stress-controlled stepwise load and stress relaxation, closed forms solutions were derived.

The class of unload and following load below the ctive process stress boundaries processes was also investigated.

For the processes belonging to this class, the close form solution, which specifies the stress-strain dependance, was also derived.

Key words: shape memory alloys, visco-plastic model with power parameter, rheonomic properties, stress-controlled and stress-controlled load processes, stress relaxation process, stress-controlled stepwise load, model calibration