Comparison of three-dimensional shape memory alloy constitutive models: Finite element analysis of actuation and superelastic responses of a shape memory alloy tube

Many three-dimensional constitutive models have been proposed to enhance the analysis and design of shape memory alloy (SMA) structural components. Phenomenological models are desirable for this purpose since they describe macroscopic responses using internal variables to govern the homogenized material response. Because they are computationally efficient on the scale of millimeters to meters, these models are often the only viable option when assessing the response of full-scale SMA components for engineering applications. Thus, many different 3D SMA constitutive models have been developed. However, for their intended user, the application engineer, a clear and straightforward methodology has not been established for selecting a model to use in a design process. A primary goal of the Consortium for the Advancement of Shape Memory Alloy Research and Technology (CASMART) modeling working group has been establishment of model selection methodology. One critical step in this process is the development of benchmark problems that clearly illustrate the capabilities and efficiencies of models. In this paper, we propose a set of benchmark problems centered on an SMA tube component. These problems have been selected to demonstrate both uniaxial and multiaxial, actuation and superelastic capabilities of 3D SMA models. We then use finite element simulations of these benchmark problems to compare and contrast both the material modeling and implementation of three unique SMA constitutive models.