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Hydrogels possess magnificent properties which may be harnessed for novel applications. However, this is not achievable if the mechanical behaviors of hydrogels are not well understood. This paper aims to provide the reader with a bird's eye view of the mechanics of hydrogels, in particular the theories associated with deformation of hydrogels, the phenomena that are commonly observed, and recent developments in applications of hydrogels. Besides theoretical analyses and experimental observations, another feature of this paper is to provide an overview of how mechanics can be applied.

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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Classical molecular dynamics with the AIREBO potential is used to investigate and compare the thermal conductivity of both zigzag and armchair graphene nanoribbons possessing various densities of Stone-Thrower-Wales (STW) and double vacancy defects, within a temperature range of 100-600 K. Our results indicate that the presence of both kinds of defects can decrease the thermal conductivity by more than 80% as defect densities are increased to 10% coverage, with the decrease at high defect densities being significantly higher in zigzag compared with armchair nanoribbons. Variations of thermal conductivity in armchair nanoribbons were similar for both kinds of defects, whereas double vacancies in the zigzag nanoribbons led to more significant decreases in thermal conductivity than STW defects. The same trends are observed across the entire temperature range tested.

Porous structures of silica aerogels are generated using classical molecular dynamics, with the Tersoff potential, which has been re-parametrized for modeling silicon dioxides. This work demonstrates that this potential is superior to the widely used BKS potential in terms of characterizing the thermal conductivities of amorphous silica, by comparing the vibrational density of states with previous experimental studies. Aerogel samples of increasing densities are obtained through an expanding, heating and quenching process. Reverse non-equilibrium molecular dynamics is applied at each density to determine the thermal conductivity. A power-law fit of the results is found to accurately reflect the power-law variation found in experimental bulk aerogels. The results are also of the same order of magnitude as experimental bulk aerogels, but they are consistently higher. By analyzing the pore size distribution on different simulation length scales, we show that such a disparity is due to finite sizes of pores that can be represented, where increasing simulation length scales lead to an increase in the largest pore size that can be modeled.