Zhang Wei, Ma Yueyin, Gao Xinyu, Chen Wanhua, Nie Xutao
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China.
China Aerodynamics Research and Development Center, Mianyang 621000, China.
Micromachines (Basel). 2022 Jun 13;13(6):939. doi: 10.3390/mi13060939.
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 () and austenite (), twinned martensite () 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.
形状记忆合金（SMA）因其伪弹性、超弹性和形状记忆效应等优点，是变形飞机潜在的驱动装置之一。对形状记忆合金进行精确快速的分析同时也成为工业应用的关键需求。在本研究中，基于扩展的博伊德 - 拉古达斯模型，实现了一个用户定义材料子程序（UMAT）并成功应用于ABAQUS中的三维数值模拟。除了传统的去孪晶马氏体（ ）和奥氏体（ ）外，还考虑了孪晶马氏体（ ）以准确模拟实际转变。然后，采用等效热应变方法来简化使用UMAT时的模拟复杂性。通过重置热膨胀系数，生成了与原始相变应变等效的热应变。该方法在两种情况下得到验证，结果与扩展的博伊德 - 拉古达斯模型一致，且时间消耗减少了89.1%。最后，设计了一种集成单量程形状记忆合金和不锈钢板的主动变形蒙皮，以实现双向变形。蒙皮计算得到的弧高变化为3.74 mm，与3.81 mm的实验结果相比，相对误差为1.84%。UMAT与等效热应力方法的联合使用有助于降低形状记忆合金建模的难度。
