Weak enforcement of interface continuity and generalized periodicity in high?order electromechanical problems

We present a formulation for the weak enforcement of continuity conditions at material interfaces in high-order problems by means Nitsche's method, which is particularly suited unfitted discretizations. This extended to impose generalized periodicity unit cell boundaries periodic structures. The derived flexoelectricity, electromechanical coupling between strain gradient and electric field, mathematically modeled as coupled system fourth-order PDEs. design flexoelectric devices requires solution boundary value on complex architectures, including general multimaterial arrangements. can be efficiently achieved with an immersed B-splines approach. Furthermore, metamaterials also involves analysis cells conditions. Optimal convergence rates are obtained B-spline approximation, confirming reliability method. numerical simulations illustrate usefulness proposed approach toward functional harnessing effect.