A comprehensive review on thermomechanical constitutive models for shape memory polymers

Shape memory polymers are a class of smart materials, which are capable of fixing their deformed shapes, and can return to their original shape in reaction to external stimulus such as heat. Also due to their exceptional properties, they are mostly used in four-dimensional printing applications. To model and investigate thermomechanical response of shape memory polymers mathematically, several constitutive equations have been developed over the past two decades. The purpose of this research is to provide an up-to-date review on structures, classifications, applications of shape memory polymers, and constitutive equations of thermally responsive shape memory polymers and their composites. First, a comprehensive review on the properties, structure, and classifications of shape memory polymers is conducted. Then, the proposed models in the literature are presented and discussed, which, particularly, are focused on the phase transition and thermo-viscoelastic approaches for conventional, two-way as well as multi-shape memory polymers. Then, a statistical analysis on constitutive relations of thermally activated shape memory polymers is carried out. Finally, we present a summary and give some concluding remarks, which could be helpful in selection of a suitable shape memory polymer constitutive model under a typical application.