Design of a Morphing Skin with Shape Memory Alloy Based on Equivalent Thermal Stress Approach

Shape memory alloy (SMA) is one of the potential driving devices for morphing aircraft due to its advantages of pseudoelasticity, superelasticity, and shape memory effect. Precise and fast analysis of SMA has simultaneously become a key requirement for industrial applications. In this study, a user-defined material subroutine (UMAT) was implemented and successfully applied in a three-dimensional numerical simulation in ABAQUS based on the extended Boyd-Lagoudas model. In addition to the conventional detwinned martensite (M_d) and austenite (A), twinned martensite (M_t) was also considered to model the practical transformation accurately. Then, the equivalent thermal strain approach was adopted to simplify the simulation complexity with UMAT. By resetting the thermal expansion coefficient, the thermal strain equivalent to the original phase transformation strain was generated. The approach was validated in two cases, showing consistent results with the extended Boyd-Lagoudas model and reduction in time consumption by 89.1%. Lastly, an active morphing skin integrating the single-range SMA and a stainless-steel plate was designed to realize two-way morphing. The calculated arc height variation of the skin was 3.74 mm with a relative error of 1.84% compared to the experimental result of 3.81 mm. The coupled use of UMAT and the equivalent thermal stress approach helped to reduce the challenge in modeling SMA.