We present an energy-based low-cycle fatigue criterion that can be used in analyzing
and designing structures made from shape memory alloys subjected to cyclic loading.
Experimentally, a response similar to plastic shakedown is observed. During the first
cycles the stress-strain curve shows a hysteresis loop which evolves during the first
few cycles before stabilizing. By adopting an analogy with plastic fatigue, it is shown
that the dissipated energy of the stabilized cycle is a relevant parameter for
estimating the number of cycles to failure of such materials. Following these
observations, we provide an application of the cyclic model, previously developed by
the authors within the framework of generalized standard materials with internal
constraints in order to evaluate such parameter. Numerical simulations are
presented along with a validation against experimental data in case of cyclic
superelasticity.