This work aims to provide a comprehensive review of the continuum models of the phase behaviors of liquid crystal networks (LCNs), novel materials with various engineering applications thanks to their unique composition of polymer and liquid crystal. Two distinct behaviors are primarily considered: soft elasticity and spontaneous deformation found in the material. First, we revisit these characteristic phase behaviors, followed by an introduction of various constitutive models with diverse techniques and fidelities in describing the phase behaviors. We also present finite element models that predict these behaviors, emphasizing the importance of such models in predicting the material’s behavior. By disseminating various models essential to understanding the underlying physics of the behavior, we hope to help researchers and engineers harness the material’s full potential. Finally, we discuss future research directions necessary to advance our understanding of LCNs further and enable more sophisticated and precise control of their properties. Overall, this review provides a comprehensive understanding of the state-of-the-art techniques and models used to analyze the behavior of LCNs and their potential for various engineering applications.

Nematic liquid crystalline solids are novel smart materials of which mesogenic molecules are incorporated within their polymeric chains via crosslinking. The material exhibits many interesting phase behaviors and is envisaged to be harnessed as a key material of soft responsive structures that are adaptive to their surroundings. These behaviors are originated by intricate interactions between diverse phenomena ranging from molecular interactions, mesoscopic phase transition, and elasticity of macroscale. The modeling and analysis of the behavior, therefore, requires the multiscale point of view in that the vast design space of such material cannot be fully exploited otherwise. In this regard, the multiscale behaviors of the nematic solids are first visited, elucidating qualitative behaviors and research of individual physics. Further, the multiscale analysis approach applied to understand and harness the behaviors of the nematic liquid crystalline solids is then reviewed.