Computational modeling and rational design of flexoelectric metamaterials and devices

Abstract

Piezoelectricity, the two-way coupling between electric polarization and strain is the basic
 mechanism behind most electromechanical transduction technologies. It is possible only
 in a limited number of materials, namely those exhibiting a non-centrosymmetric atomic
 or molecular structure. Flexoelectricity, the two-way coupling between strain gradient and
 polarization, and conversely polarization gradient and strain, is a universal property of all
 dielectrics. For most materials the flexoelectric coupling is relatively weak, and thus requires
 large gradients, which are attainable at small scales. Flexoelectricity thus provides a route to
 design alternative materials and devices for electromechanical transduction exploiting field
 gradients at small scales, by itself or as a complement to piezoelectricity. It also broadens the
 class of materials that can be used in these applications, overcoming the limitations of piezoelectrics
 regarding biocompatibility, toxicity and operating temperature. The present thesis
 focuses on exploring theoretically the engineering concepts for the rational design of piezoelectric
 metamaterials and devices exploiting the flexoelectric effect in general dielectrics,
 including non-piezoelectrics.
 This work relies on the premise that the material polarity required for an effective piezoelectric
 response, can be imprinted in the metamaterial through material architecture at
 the microscale, thus eliminating the need for a non-centrosymmetric atomic and molecular
 structure of the base-material. This concept is explored in detail and demonstrated in the
 thesis through accurate self-consistent simulations, showing that significant effective piezoelectricity
 can be achieved in non-piezoelectrics by accumulating the flexoelectric response
 of small features under bending or torsion. This thesis proposes low area-fraction bendingdominated
 piezoelectric 2D periodic lattice metamaterial designs. The effective piezoelectric
 response is quantified and the effect of lattice geometry, orientation, feature size and areafraction
 is revealed. Through computational homogenization, the full effective piezoelectric
 tensor is characterized, and a simple shape optimization study is presented, showing significant
 enhancements relative to the initial designs. Designs for flexoelectric devices combining
 multiple materials are also proposed, analyzed and quantified. As a possible building
 block for three-dimensional metamaterials, the flexoelectric response of bars under torsion
 is studied in detail, identifying the conditions under which such a response is possible. Furthermore,
 this study has allowed us to propose an experimental setup to quantify the elusive
 shear flexoelectric coefficient, one of the three independent components in cubic flexoelectric
 systems Este trabajo se basa en la premisa de que la polaridad del material requerida para una respuesta piezoeléctrica efectiva, puede imprimirse en el metamaterial a través de la arquitectura del material a microescala, eliminando así la necesidad de una estructura atómica y molecular no centrosimétrica del material base. Este concepto se explora en detalle y se demuestra en la tesis a través de simulaciones precisas y autoconsistentes, mostrando que se puede lograr una piezoelectricidad efectiva significativa en materiales no piezoeléctricos mediante la acumulación de la respuesta flexoeléctrica de pequeñas características bajo flexión o torsión. Esta tesis propone diseños de metamateriales piezoeléctricos 2D de celosía periódica de baja fracción de área dominada por la flexión. Se cuantifica la respuesta piezoeléctrica efectiva y se revela el efecto de la geometría, la orientación, el tamaño de los elementos caracteristicos y la fracción de área. A través de la homogeneización computacional, se caracteriza el tensor piezoeléctrico efectivo completo, y se presenta un estudio de optimización de forma simple, que muestra mejoras significativas en relación con los diseños iniciales. También se proponen, analizan y cuantifican diseños de dispositivos flexoeléctricos que combinan múltiples materiales. Como posible bloque de construcción para metamateriales tridimensionales, se estudia en detalle la respuesta flexoeléctrica de barras sometidas a torsión, identificando las condiciones en las que dicha respuesta es posible. Además, este estudio nos ha permitido proponer un montaje experimental para cuantificar el elusivo coeficiente flexoeléctrico de cizalla, uno de los tres componentes independientes en los sistemas flexoeléctricos cúbicos.

A novel 3D mixed finite element for flexoelectricity in piezoelectric materials

“…48 To circumvent the existing issue of torsion of flexoelectric cylindrical bars, a truncated semicone structure was proposed. 49,50 Due to the variation of the cross section along the axis of the semicone, strain gradients ηZZR and ηZZT (in the cylindrical coordinate system) are the most prominent ones enabling flexoelectricity to occur. A cylindrical coordinate system is defined by R − T − Z, with R representing the radial axis, T denoting azimuth, and Z-the axial coordinate.…”

Mathematical and computational modeling of flexoelectricity at fixed and moving interfaces, fracture surfaces and contact

“…A natural choice is torsion of flexoelectric bars. Nevertheless, torsion-induced strain gradients result in vanishing flexoelectric response in cubic systems, regardless of the shape of the bar's cross-section (Mocci, 2021, Mocci et al, 2023. A significant response can be obtained by considering a varying cross-section, although the response, in this case, involves all three flexoelectric modes, and a carefully derived correction is needed, as seen in Mocci et al (2023).…”