Direct numerical determination of the asymptotic cyclic behavior of pseudoelastic shape memory structures

The design of shape memory alloys (SMAs) structures against fatigue requires the computation of the stabilized mechanical state. The classical computation method, based on a plasticity-like algorithm, requires a step-by-step calculation, leading to prohibitive computation time to reach this stabilized state. To overcome this issue, we propose to extend the direct cyclic method (DCM), for elastoplastic structures, for use with the Zaki-Moumni (ZM) model for SMAs. DCM is a large time increment method in which a periodicity condition is enforced on the state variables. Comparison with the classical incremental approach shows considerable reduction in computation time.