Topology optimization of nonlinear flexoelectric structures

Recent advances in nanotechnology have allowed for the manufacturing of nanostructures and nanodevices with optimized topologies that outperforms their traditional counterparts based on simple geometry in terms of efficiency and function. In this work, a novel nonlinear topology optimization procedure is developed to design optimal layouts of flexoelectric structures un-dergoing large displacement. The optimal material distribution is determined by optimizing the energy conversion efficiency. Two material properties such as the elasticity coefficient and the permittivity coefficient are interpolated through the solid isotropic material with a penalization approach via an energy interpolation scheme to overcome the numerical instability. Obtained results have revealed that accounting for the geometric nonlinearity leads to a different final optimal topology with a better energy converting efficiency as compared to the linear model. We also found the significant influences of size effects on the optimized structure emphasizing the importance of nonlocal elastic behavior in characterizing and designing micro-structures and flexoelectricity.