This paper presents the development and implementation of a user-defined material (UMAT) model for NiTi Shape-Memory Alloy (SMA) wires for use in LS-DYNA commercial explicit finite-element analysis software. The UMAT focusses on the Shape-Memory Effect (SME), which could be used for actuation of aerostructural components. The actuation of a fundamental structure consisting of an SMA wire connected in series with a linear spring was studied first. The SMA thermomechanical behaviour obtained from the finite-element simulation was compared with that obtained from the analytical solution in MATLAB. A further comparison is presented for an SMA-actuated cantilever beam, showing excellent agreement in terms of the SMA stress and strain as well as the tip deflection of the cantilever beam. A mesh sensitivity study on the SMA wire indicated that one beam element was adequate to accurately predict the SMA thermomechanical behaviour. An analysis of several key parameters showed that, to achieve a high recovery strain, the stiffness of the actuated structure should be minimised while the cross-sectional area of the SMA wire should be maximised. The actuation of an SMA wire under a constant stress/load was also analysed. The SMA material model was finally applied to the design of morphing aluminium and composite aerofoils consisting of corrugated sections, resulting in the prediction of reasonably large trailing-edge deflections (7.8–65.9 mm).

中文翻译：

---

用于变形机翼的 NiTi 形状记忆线的有限元建模

本文介绍了用于 LS-DYNA 商用显式有限元分析软件的 NiTi 形状记忆合金 (SMA) 线的用户定义材料 (UMAT) 模型的开发和实施。UMAT 专注于形状记忆效应 (SME)，可用于驱动航空结构部件。首先研究了由与线性弹簧串联的 SMA 线组成的基本结构的驱动。将从有限元模拟获得的 SMA 热机械行为与从 MATLAB 中的解析解获得的进行比较。进一步比较了 SMA 驱动的悬臂梁，在 SMA 应力和应变以及悬臂梁的尖端偏转方面显示出极好的一致性。对 SMA 线的网格敏感性研究表明，一个梁单元足以准确预测 SMA 热机械行为。对几个关键参数的分析表明，为了实现高恢复应变，驱动结构的刚度应最小化，而 SMA 线的横截面积应最大化。还分析了在恒定应力/负载下 SMA 线的驱动。SMA 材料模型最终应用于由波纹截面组成的变形铝和复合机翼的设计，从而预测出相当大的后缘偏转（7.8-65.9 毫米）。驱动结构的刚度应最小化，而 SMA 线的横截面积应最大化。还分析了在恒定应力/负载下 SMA 线的驱动。SMA 材料模型最终应用于由波纹截面组成的变形铝和复合机翼的设计，从而预测出相当大的后缘偏转（7.8-65.9 毫米）。驱动结构的刚度应最小化，而 SMA 线的横截面积应最大化。还分析了在恒定应力/负载下 SMA 线的驱动。SMA 材料模型最终应用于由波纹截面组成的变形铝和复合机翼的设计，从而预测出相当大的后缘偏转（7.8-65.9 毫米）。