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.

Simulation of Shape Memory Alloy (SMA)-Bias Spring Actuation for Self-Shaping Architecture: Investigation of Parametric Sensitivity

“…It is evident that MVF, a function of material temperatures, is crucial to the mechanical behavior of SMAs (Figure 6), as it is directly involved with the elastic modulus. By the same token, actuator output performance tends to depend mainly on the bound of the terminal operating temperatures, which is similar to the findings of a previous study using the Ivshin-Pence model [29]. To obtain the desired output stroke and force, Figure 6 and Section 3.6 suggest that SMA ingredients be properly manufactured for the R-phase M s to be no greater than A s so that elongation and recovery are clearly separated in the morphing of the internal SMA structures.…”

Position Measurements Using Magnetic Sensors for a Shape Memory Alloy Linear Actuator

“… Temperature estimation of the SMA spring: In this work, the temperature was just measured on a specific place of the spring, and the obtained information was just acquired in order to avoid damages in the mechanical structure by the overheat during the activation of the actuator. However, the temperature on the SMA spring could be described by a model of distributed parameters where the temperature over the spring is not assumed to be uniform [ 50 , 51 ]. The estimation of parameters from this class of systems requires a highly complex computation effort [ 52 , 53 ].…”

Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

“…Variance-based SA (generally called Sobol SA) introduces uncertainty as variance and decomposes the variance of the output of the model or system into portions that can be attributed to inputs or sets of inputs [2,3]. Sobol SA is very popular; the principles of the method are often mentioned [4][5][6][7][8] and many articles have applied Sobol SA in their research [9][10][11][12][13].…”