Shakedown theorems for shape memory alloys structures with functional fatigue-Application to nitinol stents

Shape memory alloys (SMAs) offer interesting perspectives in various fields such as aeronautics, robotics, biomedical sciences, or structural engineering. The distinctive properties of those materials stem from a solid/solid phase transformation occurring at a microscopic level. Modeling the rather complex behavior of SMAs is a topic of active research. Lately, SMA models coupling phase-transformation with permanent inelasticity have been proposed to capture degradation effects which are frequently observed experimentally for cyclic loadings - a phenomenon referred to as functional fatigue. In this paper, the classical static and kinematic shakedown of plasticity theory are extended to such material models. Those results give conditions for the energy dissipation to remain bounded, which is beneficial for the fatigue life. Analytical shakedown limits are obtained for a 3-bar truss example and compared with numerical results from step-by-step simulations. We consider the problem of a nitinol stent submitted to cyclic pressure and mixed pressure- bending as an application, showing how the approach presented can be combined with finite-element analysis to study shakedown of complex 3D structures.