  In this work, a thermo-mechanical model that predicts the actuation response
of shape memory alloys is probabilistically calibrated against three
experimental data sets simultaneously. Before calibration, a design of
experiments (DOE) has been performed in order to identify the parameters most
influential on the actuation response of the system and thus reduce the
dimensionality of the problem. Subsequently, uncertainty quantification (UQ) of
the influential parameters was carried out through Bayesian Markov Chain Monte
Carlo (MCMC). The assessed uncertainties in the model parameters were then
propagated to the transformation strain-temperature hysteresis curves (the
model output) using first 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. Results show
good agreement between model and experimental hysteresis loops after
probabilistic MCMC calibration such that the experimental data are situated
within 95% Bayesian confidence intervals. 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 from running replicas around a
single new experimental condition versus running experiments in different
regions of the experimental space.
