Multi-shape memory polymers (m-SMP) and their composites, as new kind of smart materials, can change their shapes and keep the deformed states under external forces. When stimulated by specific stimuli, m-SMP and its composite can reversibly return to the original shapes. m-SMP and its composite are widely used in various complex sensing devices, biomedical, aerospace and other intelligent devices due to their advantages of large deformation, high recovery rate, easy configuration and easy adjustment of shape response temperature. In this paper, we established a new three-dimensional constitutive model for m-SMP and its composite by introducing the level-set method into viscoelastic constitutive equations. In this model, we regarded m-SMP and its composite as inhomogeneous bodies consisting of different phases and used the level-set functions to describe the phase transformation relationships. We took dual-shape memory polymer (SMP) and triple-shape memory polymeric composite (TSPC) as examples to illustrate the process of establishing the model. SMP includes two phases, glass phase and rubber phase, and TSPC includes three phases, rubbery–liquid-like phase, rubbery–semicrystalline phase and glass phase. We used the developed constitutive model to numerically simulate the complete shape memory processes and numerically simulate the mechanical behavior of each process with different correlative rates of SMP and TSPC. The simulation results of shape memory process show that the new constitutive model can describe shape memory behaviors accurately with comparing the simulated result and the existing text data. And the simulation results of each process reflect that the shape memory process has a strong rate correlation. The constitutive model established in this paper can provide a theoretical basis for the application of SMP and TSPC, and can be further extended to m-SMP and its composite.

多形状记忆聚合物（m-SMP）及其复合材料作为新型智能材料，可以在外力作用下改变形状并保持变形状态。当受到特定刺激的刺激时，m-SMP 及其复合物可以可逆地恢复到原始形状。m-SMP及其复合材料由于具有变形大、恢复率高、易配置、形状响应温度易调节等优点，被广泛应用于各种复杂传感设备、生物医学、航空航天等智能设备中。在本文中，我们通过将水平集方法引入粘弹性本构方程，建立了一种新的 m-SMP 及其复合体的三维本构模型。在这个模型中，我们将 m-SMP 及其复合体视为由不同相组成的不均匀体，并使用水平集函数来描述相变关系。我们以双重形状记忆聚合物（SMP）和三重形状记忆聚合物复合材料（TSPC）为例来说明建立模型的过程。SMP包括两相，玻璃相和橡胶相，TSPC包括三相，橡胶-类液体相、橡胶-半晶相和玻璃相。我们使用开发的本构模型对完整的形状记忆过程进行数值模拟，并在不同 SMP 和 TSPC 相关速率下对每个过程的力学行为进行数值模拟。形状记忆过程的仿真结果表明，新的本构模型可以准确地描述形状记忆行为，将仿真结果与现有文本数据进行比较。并且各个过程的仿真结果反映了形状记忆过程具有很强的速率相关性。本文建立的本构模型可为SMP和TSPC的应用提供理论依据，并可进一步推广到m-SMP及其复合材料。