A Novel Form of Imperfect Contact Laws in Flexoelectricity

Flexoelectric materials exhibit coupling between electric polarization and mechanical strain gradient. At the nano-scale and micro-scale, these materials offer a promising potential for the development of mechanical transducers and energy harvesters. This work proposes a new imperfect interface model simulating the behavior of a thin flexoelectric layer (adhesive) of vanishing thickness, embedded between two flexoelectric media (adherents). The adhesive is assumed to be mechanically compliant and electrically lowly-conducting. The interface model is obtained by using the asymptotic analysis. The contact laws, expressed in terms of the jumps and means values of the displacements, normal derivatives of the displacements, and electric potential across the interface, represent a formal generalization of the soft elastic and piezoelectric interface conditions. A simple application, considering a one-dimensional three-layer composite micro-bar subject to electro-mechanical loads, is developed in order to analytically/numerically assess the asymptotic model. Nonlocal phenomena and end-effects, related to a flexoelectric length-scale parameter, are highlighted. The example illustrates the usefulness of the proposed approach toward the design of thin nano- and microscale devices exploiting the flexoelectric effect.