Computational modelling of flexoelectricity-based 2D metamaterials

We propose a methodology to impose generalised periodicity to the solution of the flexoelectric problem in the two-dimensional metamaterials design setting. To achieve this goal, we leverage an existing model for flexoelectricity which includes strain gradient elasticity, ultimately leading to a system of 4th order PDEs. After identifying the adequate boundary conditions, we obtain a suitable weak formulation of our problem statement via a finite element approach. The aforementioned methodology is then embedded within an existing Matlab framework. Hence, we also validate and assess the performance of this implementation with a series of experiments of our own design, including convergence tests and applications to engineeringly realistic settings for which we have some prior knowledge about the results that should be expected