Size-Dependent Electro-Thermal Buckling Analysis of Flexoelectric Microbeams

This paper studies electro-thermal buckling in a flexoelectric microbeam. This first-of-a-kind study focuses on two case-specific types of buckling in microbeams, which are essential to microstructures. Because of the electric fields and high temperatures in their environments, microbeams are susceptible to electro-thermal buckling more often than mechanical buckling. In addition, microstructures can exhibit flexoelectricity. As such a thorough understanding of electro-thermal bucking is extremely important. In this paper, we begin with extracting the equations governing flexoelectric microbeams from size-dependent flexoelectric theories. We then derive closed-form solutions for said equations. We explore various boundary conditions and, with respect to the load, analyze the various pre-buckling and buckling modes. Our study shows that buckling does not occur in some boundary conditions, and electrical curvature is very important in isotropic and homogeneous flexoelectric microbeams. In the end, the paper presents electro-thermal buckling results for specific boundary conditions as well the probability of buckling.