为揭示形状记忆效应的黏弹性力学机制并进行形状记忆过程模拟，先推导出积分形式的广义Maxwell本构方程，再结合时温叠加原理推导出形状记忆过程的形状固定率公式及应力应变演化方程.形状固定率公式显示：增大“固定约束时长/拉伸阶段时长”的比值可增大形状固定率.应变演化方程揭示：随温度降低偏移系数变小，释放约束后应变演化方程中的时间被缩减，使应变恢复速度趋近于0；随温度升高偏移系数变大，对时间的缩减效应减弱，应变发生恢复.应用Abaqus软件的黏弹性力学模型，基于Arrhenius方程和Williams-Landel-Ferry(WLF)方程，通过二次开发建立形状记忆聚合物结构分析的数值模拟方法.采用环氧基形状记忆聚合物进行拉伸-松弛实验测定数值模拟中需要输入的材料参数，并进行形状记忆过程实验和数值模拟.结果表明，所提数值模拟方法能有效描述形状记忆过程，且针对实验所用的环氧基形状记忆聚合物，Arrhenius方程较WLF方程具有更高的计算精度.
In order to reveal the viscoelastic mechanism and conduct simulation of SM (shape memory) effect, the stress and strain evolutions and fixity ratio equation were derived from the generalized Maxwell model with time temperature superposition principle. Fixity ratio equation shows that the shape fixity ratio can be lifted by raising the ratio of holding time over tension time. The evolution equations reveal the viscous-elastic nature of the SM effect. The shift function is decreased because of the dropping of temperature, which will reduce the actual time and result in delaying of shape recovery. When the temperature raise up, the reducing effect is weakened, the shape recovery will occur. Simulation methods are established based on the viscoelastic model in Abaqus and user subroutine of Arrhenius equation and WLF equation. The material parameters of epoxy shape memory polymer are obtained by tension-relaxation tests. Then the test and simulation of SM process were conducted. Results indicate that the simulation methods are accurate enough, and Arrhenius equation results in more accurate simulations than WLF equation for epoxy SMP used in the tests.
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