A Probabilistic Approach with Built-in Uncertainty Quantification for the Calibration of a Superelastic Constitutive Model from Full-field Strain Data

Abstract

We implement an approach using Bayesian inference and machine learning to calibrate the material parameters of a constitutive model for the superelastic deformation of NiTi shape memory alloy. We use a diamond-shaped specimen geometry that is suited to calibrate both tensile and compressive material parameters from a single test. We adopt the Bayesian inference calibration scheme to take full-field surface strain measurements obtained using digital image correlation together with global load data as an input for calibration. The calibration is performed by comparing these two experimental quantities of interest with the corresponding results from a simulation library built with the superelastic forward finite element model. We present a machine learning based approach to enrich the simulation library using a surrogate model. This improves the calibration accuracy to the extent permitted by the accuracy of the underlying material model and also improves the computational efficiency. We demonstrate, verify, and partially validate the calibration results through various examples. We also demonstrate how the uncertainty in the calibrated superelastic material parameters can propagate to a subsequent simulation of fatigue loading. This approach is versatile and can be used to calibrate other models of superelastic deformation from data obtained using various modalities. This probabilistic calibration approach can become an integral part of a framework to assess and communicate the credibility of simulations performed in the design of superelastic NiTi articles such as medical devices. The knowledge obtained from this calibration approach is most effective when the limitations of the underlying model and the suitability of the training data used to calibrate the model are understood and communicated.