Apparent Flexoelectricity Due to Heterogeneous Piezoelectricity

Abstract

Recent work has highlighted how the phenomenon of flexoelectricity can masquerade as piezoelectricity. This notion can not only be exploited to create artificial piezoelectric-like materials without using piezoelectric materials, but may also explain measurement artifacts in dielectrics. In this article, we show that the reverse is also possible and potentially advantageous in certain situations (such as energy harvesting). By constructing a computational homogenization approach predicated on the finite element method, we argue that composites made of piezoelectric phases can conspire to endow the material with a distinct overall flexoelectric-like response even though the native flexoelectricity of the constituent materials is negligible. Full finite element procedures for numerical evaluation of the different effective tensors, including the flexoelectric tensor, are provided. Numerical investigations are conducted, showing variation of the effective flexoelectric properties with respect to local geometry and properties of the composite in piezoelectric-piezoelectric and polymer-piezoelectric composites. We find that the flexoelectric response can be tuned to nearly {five times} higher than the constituents.

Topology optimization of flexoelectric composites using computational homogenization

“…In this section, we review the computational homogenization framework proposed in our previous work [63] for piezoelectric composites with effective flexoelectric behavior.…”

“…r = E 0 i jk ∇ε jki (10) are body forces added to remove spurious fluctuations in the case of homogeneous RVEs (see [66] and [63] for more details). Above, σ and d are given by Eqs.…”

“…In our previous work [63], a general energy density function for an effective piezoflexoelectric material was proposed, extending a Mindlin strain gradient model with electromechanical terms as:…”

“…In the present work, we propose a topology optimization framework to design periodic composites comprised of piezoelectric constituents that exhibit large flexoelectric constants. The approach leverages a recently-developed computational homogenization framework for effective flexoelectric materials [63] that enables the estimation of the (apparent) effective flexoelectric properties of a periodic composite made of piezoelectric phases. The different associated sensitivity expression are derived in this context and a SIMP (Solid Isotropic Material with Penalization) topology optimization framework is developed.…”

Compact explicit matrix representations of the flexoelectric tensor and a graphic method for identifying all of its rotation and reflection symmetries

“…In parallel with these experimental works, theoretical studies were also conducted to demonstrate the size-dependent flexoelectric properties and surface effect of dielectric materials/structures in nanoscale, for example, by Sahin and Dost 18 , Tagantsev 19,20 , Yurkov and Tagantsev 21 , He et al 22 , Qi et al 23 and Bai et al 24 . Numerical approaches were elaborated according either to the first-principles method, for example, by Maranganti and Sharma 25 , Hong et al 26,27 or to the other theoretical calculation methods such as finite element method by Deng et al 28 and Yvonnet et al 29 , phase-field method by Li et al 30 and Wang et al 31 to estimate the flexoelectric properties of some dielectric materials/structures. For more references about flexoelectricity and for discussions on potential important applications of flexoelectricity, the reader is referred to Tagantsev et al 20 , Sharma et al 32 , Zubko et al 33 , Wang et al 34 , Narvaez et al 35 , Abdollahi et al 36 and Shu et al 37,38 .…”