显式方法精确模拟形状记忆聚合物热力学行为

通过构建一个热耦合的多轴可压缩应变能函数，得到应力-应变、应力-温度和应变-温度之间的函数关系，建立形状记忆聚合物的本构方程.本文引入三个基于对数应变的不变量使得模型（i）可以模拟可压缩情况；（ii）适用于单轴拉伸和等双轴拉伸至少两个基准实验；（iii）多轴有效.通过显式方法（i）给出自由能和熵的具体表达，证明模型热力学定律；（ii）给出应变-应力，温度-应力以及，温度-应变的形函数具体表达.多轴模型在特定的情况下可以自动退化到各自的单轴情况. 通过调节形函数的参数，最终得到的模型结果和实验结果能够精确匹配.新方法建立的本构模型得到的结果能更加准确地指导形状记忆聚合物的工程设计。

Accurately modeling thermomechancial behavior of shape memory polymer by explicit method

A constitutive model for shape memory polymer is established by constructing a multi-axial compressible strain energy with thermal-coupled property to obtain relationships between stress-strain、stress-temperature and strain-temperature. Three invariants based on Hencky strain are introduced to (i) simulate compressible condition; (ii) applicable to at least two deformation mode, i.e. uniaxial tension and compression and bi-axial tension; (iii) effective for multi-axial case. By using explicit method to (i) give out the explicit formulations of free energy and entropy to prove that the constitutive equations satisfy the thermodynamic conditions; (ii) give out the shape functions of stress-strain、stress-temperature、and strain-temperature. The multi-axial model can automatically reduce to their uniaxial case, respectively. The model result can accurately match the experiment data by adjust parameters in the shape functions. The new constitutive model can accurately guide engineer designing for the shape memory polymer.