Isogeometric topology optimization of flexoelectric materials based on perturbation analysis

Flexoelectricity is a scale-dependent phenomenon that becomes increasingly significant at smaller scales. With the growing trend toward the miniaturization of electronic devices, this characteristic enables the tailoring of material properties through microscale design to meet specific application requirements. We propose an innovative isogeometric topology optimization framework based on perturbation analysis for the design of flexoelectric materials. The framework utilizes second-order computational homogenization to determine equivalent material parameters and performs direct sensitivity analysis. Inspired by the level set method, this density-based approach incorporates a heuristic density threshold scheme to achieve clear separation between material phases. The proposed framework provides a robust and computationally efficient platform for flexoelectric material design. Numerical simulations demonstrate enhanced flexoelectric effects and the generation of equivalent piezoelectric materials, highlighting the potential of this method for advancing microscale material engineering applications.