Uncertainty quantification of the parameters and predictions of a phenomenological constitutive model for thermally induced phase transformation in Ni-Ti shape memory alloys
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2019 IOP Publishing Ltd. In this work, a probabilistic calibration approach has been adopted to quantify the uncertainties of the parameters and predictions of a phenomenological shape memory alloys (SMAs) constitutive model which has been used to predict the thermally induced phase transformation of Ni-Ti SMAs. Furthermore, the impact of the adopted calibration method, which enables the determination of the uncertainty bounds of the model predictions, on the design of robust engineering applications has been discussed. To this end prior to the probabilistic model calibration, a design of experiments has been performed in order to identify the most influential parameters on the response of the system and thus reduce the dimensionality of the problem. Subsequently, uncertainty quantification (UQ) of the influential parameters has been carried out through Bayesian Markov Chain Monte Carlo (MCMC). The assessed uncertainties in the model parameters has been then propagated to the model predictions using an approximate approach based on the variance-covariance matrix of the MCMC-calibrated model parameters and then an explicit propagation of uncertainty through MCMC-based sampling. The determined 95% Bayesian confidence intervals of the model predictions, by the latter methods, have been demonstrated and compared. Additionally, good agreement between the experimentally measured and model predicted SMA hysteresis loops has been observed where the experimental data are situated within the predicted 95% Bayesian confidence intervals. Finally, the application of the MCMC-based UQ/UP approach in decision making for experimental design has also been shown by comparing the information that can be gained by performing multiple repetitive experiments under identical thermo-mechanical conditions versus experiments under different conditions.
