A staggered explicit-implicit isogeometric formulation for large deformation flexoelectricity

Abstract

Flexoelectricity is an electromechanical coupling occurring in dielectric materials that has recently attracted significant attention. The flexoelectric effect is described by a coupled, higher-order electromechanical set of equations that have typically been solved using a computationally expensive monolithic formulation. In the present work, we propose a staggered, explicit-implicit formulation that both significantly reduces the computational expense, while enabling the capturing of electromechanical instabilities through the usage of inertia. The higher order equations are discretized using an isogeometric formulation, and we demonstrate via two numerical examples the combination of increased computational efficiency with comparable accuracy that is gained from the proposed formulation as compared to the standard monolithic approaches.