Parametric Analysis of a Phenomenological Constitutive Model for Thermally Induced Phase Transformation in Ni-Ti Shape Memory Alloys

TL;DR

This paper develops a probabilistic thermo-mechanical model for Ni-Ti shape memory alloys, calibrates it with experimental data, and quantifies uncertainties to improve predictive accuracy and experimental design decisions.

Contribution

It introduces a Bayesian MCMC-based uncertainty quantification approach for a phenomenological model of Ni-Ti alloys, enhancing predictive reliability and experimental planning.

Findings

Model predictions align with experimental hysteresis within 95% confidence intervals.

Uncertainty propagation improves understanding of parameter influence on actuation response.

Bayesian approach aids in optimizing experimental design and decision making.

Abstract

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.