A neural network model for shape memory alloy actuation response with physical constraints for partial phase transformation

In this work, we demonstrate a data-based Machine Learning (ML) framework that can capture the strain evolution during Shape Memory Alloy (SMA) actuation with a minimum of four state variable inputs.These inputs describe the thermomechanical stress-strain state of the SMA and changes in the stress state during thermal actuation. Furthermore, we identify the physics-based constraints to incorporate partial phase transformation and make predictions beyond the training regime. The ML framework uses a recurrent neural network (RNN) model to capture the nonlinear strain rate variation during phase transformation. Physics-based constraints are introduced in the RNN model to include the activation of thermoelasticity, while unloading away from transformation surfaces within the thermoelastic domain. The framework is trained using experimental thermal cycle responses of a NiTiHf SMA at different stress levels. The framework can then accurately predict actuation responses undergoing complete and partial phase transformations, and also extrapolate responses for new thermal cycling that involve complex thermomechanical loading paths. An uncertainty quantification analysis using ensemble training of the NN model is also presented to show the variability of the framework.