Analysis of One-Dimensional Ivshin–Pence Shape Memory Alloy Constitutive Model for Sensitivity and Uncertainty

Abstract

Shape memory alloys (SMAs) are classified as smart materials due to their capacity to display shape memory effect and pseudoelasticity with changing temperature and loading conditions. The thermomechanical behavior of SMAs has been simulated by several constitutive models that adopted microscopic thermodynamic or macroscopic phenomenological approaches. The Ivshin−Pence model is one of the most popular SMA macroscopic phenomenological constitutive models. The construction of the model requires involvement of parameters that possess inherent uncertainty. Under varying operating temperatures and loading conditions, the uncertainty in these parameters propagates and, therefore, affects the predictive power of the model. The propagation of uncertainty while using this model in real-life applications can result in performance discrepancies or failure at extreme conditions. In this study, we employed a probabilistic approach to perform the sensitivity and uncertainty analysis of the Ivshin−Pence model. Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods were used to perform the sensitivity analysis for simulated isothermal loading/unloading at various operating temperatures. It is evident that the model’s prediction of the SMA stress−strain curves varies due to the change in operating temperature and loading condition. The average and stress-dependent sensitivity indices present the most influential parameters at several temperatures.

Keywords

• shape memory alloy
• ivshin model
• pence model
• sensitivity analysis
• uncertainty analysis
• sma
• shape memory alloy constitutive model
• sma model
• shape memory alloy behavior