**3. Models**

Typically, the stress increases gradually during transformation, and this transformation hardening is enhanced by increasing the strain rate. In those models that did not directly consider the strain rate effect [90–93], the enhanced transformation hardening was modeled by a phenomenological hardening function with parameters fitted for different strain rates rather than a physical model that inherently considers the hardening mechanism. The hardening function provided extra resistance to transformation, and was generally described as a function of internal state variables with temperature-dependent parameters. These parameters were calibrated by experiments under a specific strain rate and needed to be updated when the strain rate changed. As a result, these models could only give accurate predictions in cases of limited change of the strain rate with a specific group of parameters.

To directly account for the strain rate effects discussed in Section 2, thermal source models are proposed for modeling the NiTi SMA behaviors at low and medium strain rates, and as extended versions, thermal kinetic models are proposed for high strain rates to consider the kinetic effect in shock conditions. These models that take account of the selfheating mechanism and represent the strain rate effect by means of thermal sources can be termed as thermal source models. This is because the strain rate influences the martensitic transformation rate, in turn influences the heat production rate and temperature field. In shock conditions, the velocity of dislocations and phase interfaces set in, so the thermal source model has been extended to thermal kinetic models to consider these kinetic effects.
