针对超弹性记忆合金(SMA)螺旋结构的实际应用，基于现有的描述轴向拉伸变形的解析模型和简化后的SMA材料本构关系，采用等效转换法，建立均匀外部径向载荷下螺旋结构收缩变形与轴向拉伸变形的联系，得到描述径向收缩变形时线圈半径随外部均匀径向载荷变化的解析模型.通过与有限元数值分析的对比，验证了该解析模型的准确性.将所提出解析模型推广到螺旋编织结构介入治疗支架的实际应用中，通过参数化分析及与有限元数值模拟结果的对比，讨论其适用性，并进行误差分析.由于采用解析函数描述SMA螺旋结构的径向收缩变形特征，便于螺旋结构前期设计时针对目标进行参数调整，所以该理论模型的计算效率优于有限元分析方法.
Based on the analytical models which describe axial extension on both ends of superelastic shape memory alloy (SMA) helical structures and the simplified constitutive model of SMA materials, in this paper, the equivalent-transformed method is applied to establish the relationship between the shrinkage of helical springs undergoing uniform radial pressure and the axial extension deformation, with the purpose of satisfying the practical application of helical structures made of SMA. The validity is proved through finite element method (FEM) and then this analytical model is generalized to braided stents for inter interventional therapy. The possibility of this application and error analysis are discussed through parametric analysis and comparison between results of analytical model and FEM. This model can be applied to analyze the deformation behavior of radial compression of SMA helical springs in an analytical way, and its computational efficiency is obviously superior to FEM, so that it is more convenient to adjust parameters to achieve the desired deformation in earlier stage of helical structure design.
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