Physics-informed deep operator network for predicting martensite evolution in superelastic shape memory alloys through cyclic tensile tests

Superelastic shape memory alloy (SMA) wires and rods possess unique deformation and energy dissipation capabilities. For the assessment of their stress response, commonly cyclic tensile tests are conducted. An important but subtle parameter in this procedure is the martensite evolution. In scenarios where conducting thermal experiments is impractical, inverse modeling from cyclic tests serves as a viable alternative. However, employing constitutive models in this process presents distinct challenges, such as parameter identification and calibration, or numerical stability issues. To address these challenges, this paper proposes a data-driven method based on a physics-informed deep operator network (DeepONet) to estimate the martensite evolution. Constraint with a stress equation, the network requires only strain–stress data for training and provides stress responses in addition to the martensite evolution. From the training data, the network learns to consider the effects included in the response. The DeepONet can be coupled with experiments to provide online estimates from noisy sensor-based strain inputs, while remaining numerically stable. Moreover, this approach avoids the need for separate parameter identification or calibration. This paper details this method and evaluates its performance through experiments conducted on superelastic SMA wires. Furthermore, as an alternative approach, training using a constitutive model is provided.