Hydrogels and shape memory polymers (SMPs) possess excellent and interesting properties that may be harnessed for future applications. However, this is not achievable if their mechanical behaviors are not well understood. This paper aims to discuss recent advances of the constitutive models of hydrogels and SMPs, in particular the theories associated with their deformations. On the one hand, constitutive models of six main types of hydrogels are introduced, the categorization of which is defined by the type of stimulus. On the other hand, constitutive models of thermal-induced SMPs are discussed and classified into three main categories, namely, rheological models; phase transition models; and models combining viscoelasticity and phase transition, respectively. Another feature in this paper is a summary of the common hyperelastic models, which can be potentially developed into the constitutive models of hydrogels and SMPs. In addition, the main advantages and disadvantages of these constitutive modes are discussed. In order to provide a compass for researchers involved in the study of mechanics of soft materials, some research gaps and new research directions for hydrogels and SMPs constitutive modes are presented. We hope that this paper can serve as a reference for future hydrogel and SMP studies.

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