Liquid crystal elastomers (LCEs) are a type of material with specific features of polymers and of liquid crystals. They exhibit interesting behaviors, i.e., they are able to change their physical properties when met with external stimuli, including heat, light, electric, and magnetic fields. This behavior makes LCEs a suitable candidate for a variety of applications, including, but not limited to, artificial muscles, optical devices, microscopy and imaging systems, biosensor devices, and optimization of solar energy collectors. Due to the wide range of applicability, numerical models are needed not only to further our understanding of the underlining mechanics governing LCE behavior, but also to enable the predictive modeling of their behavior under different circumstances for different applications. Given that several mainstream methods are used for LCE modeling, viz. finite element method, Monte Carlo and molecular dynamics, and the growing interest and reliance on computer modeling for predicting the opto-mechanical behavior of complex structures in real world applications, there is a need to gain a better understanding regarding their strengths and weaknesses so that the best method can be utilized for the specific application at hand. Therefore, this investigation aims to not only to present a multitude of examples on numerical studies conducted on LCEs, but also attempts at offering a concise categorization of different methods based on the desired application to act as a guide for current and future research in this field.

The high current densities in today's microelectronic devices and microchips lead to hotspot formations and other adverse effects on their performance. Therefore, a computational tool is needed to not only analyze but also accurately predict spatial and temporal temperature distribution while minimizing the computational effort within the chip architecture. In this study, a proper orthogonal decomposition (POD)-Galerkin projection-based reduced order model (ROM) was developed for modeling transient heat transfer in three-dimensional (3D) microchip interconnects. comsol software was used for producing the required data for ROM and for verifying the results. The developed technique has the ability to provide accurate results for various boundary conditions on the chip and interconnects domain and is capable of providing accurate results for nonlinear conditions, where thermal conductivity is temperature dependent. It is demonstrated in this work that a limited number of observations are sufficient for mapping out the entire evolution of temperature field within the domain for transient boundary. Furthermore, the accuracy of the results obtained from the developed ROM and the stability of accuracy over time is investigated. Finally, it is shown that the developed technique provides a 60-fold reduction in simulation time compared to finite element techniques.