Sensitivity and Uncertainty Analysis of One-Dimensional Tanaka and Liang-Rogers Shape Memory Alloy Constitutive Models

Abstract

A shape memory alloy (SMA) can remember its original shape and recover from strain due to loading once it is exposed to heat (shape memory effect). SMAs also exhibit elastic response to applied stress above the characteristic temperature at which transformation to austenite is completed (pseudoelasticity or superelasticity). Shape memory effect and pseudoelasticity of SMAs have been addressed by several microscopic thermodynamic and macroscopic phenomenological models using different modeling approaches. The Tanaka and Liang-Rogers models are two of the most widely used macroscopic phenomenological constitutive models for describing SMA behavior. In this paper, we performed sensitivity and uncertainty analysis using Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods for the Tanaka and Liang-Rogers models at different operating temperatures and loading conditions. The stress-dependent and average sensitivity indices have been analyzed and are presented for determining the most influential parameters for these models. The results show that variability is primarily caused by a change in operating temperature and loading conditions. Both models appear to be influenced by the uncertainty in elastic modulus of the material significantly. The analyses presented in this paper aim to provide a better insight for designing applications using SMAs by increasing the understanding of these models’ sensitivity to the input parameters and the cause of output variability due to uncertainty in the same input parameters.

Keywords

• shape memory alloy
• Tanaka model
• Liang-Rogers model
• sensitivity analysis
• uncertainty analysis
• SMA
• shape memory alloy constitutive models