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Research Papers

Constructive and Destructive Interplay Between Piezoelectricity and Flexoelectricity in Flexural Sensors and Actuators

[+] Author and Article Information
Amir Abdollahi

Laboratori de Cálcul Numéric,
Departament de Matemática Aplicada III,
Universitat Politécnica de Cataluña,
Jordi Girona 1-3,
Barcelona E-08034, Spain

Irene Arias

Laboratori de Cálcul Numéric,
Departament de Matemática Aplicada III,
Universitat Politécnica de Cataluña,
Jordi Girona 1-3,
Barcelona E-08034, Spain
e-mail: irene.arias@upc.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 2, 2015; final manuscript received August 17, 2015; published online September 10, 2015. Assoc. Editor: M. Taher A. Saif.

J. Appl. Mech 82(12), 121003 (Sep 10, 2015) (4 pages) Paper No: JAM-15-1347; doi: 10.1115/1.4031333 History: Received July 02, 2015; Revised August 17, 2015

Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100 nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.

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Figures

Grahic Jump Location
Fig. 1

Piezoelectric bimorph cantilever beams consist of two identical piezoelectric layers (a) series arrangement and (b) parallel arrangement. The beams are mechanically fixed at the left-end and the mechanical point load F is applied at the right-end. In the series bimorph, the electric potential is fixed to zero at the top face while it is fixed to zero at the top and bottom faces of the parallel bimorph. An active electrode is placed at the bottom of the series bimorph and at the layers interface in the parallel bimorph. This active electrode may either fix the electric potential to a constant value (V in series and V/2 in parallel) or undergo a difference of electric potential as a result of mechanical deformation. The arrows inside the layers indicate the directions of polarization (P) and electric field (E). The polarized layers in the series bimorph can be either HH or TT while they can be polarized downward (negative, P) orupward (positive, P+) in the parallel bimorph.

Grahic Jump Location
Fig. 2

Normalized vertical displacement as a function of the normalized beam thickness for the series bimorph arrangements: TT and HH polarized layers. The results are obtained for the piezoelectric bimorphs with and without flexoelectricity. The insets show the distribution of electric field in both arrangements for different beam thicknesses.

Grahic Jump Location
Fig. 3

Normalized vertical displacement as a function of the normalized beam thickness for the parallel bimorph arrangements: negatively (P) and positively (P+) polarized layers. The results are obtained for the piezoelectric bimorphs with and without flexoelectricity. The insets show the distribution of electric field in both arrangements for different beam thicknesses.

Grahic Jump Location
Fig. 4

Normalized voltage as a function of the normalized beam thickness for the series bimorph arrangements: TT and HH polarized layers. The results are obtained for the piezoelectric bimorphs with and without flexoelectricity. The insets show the distribution of axial strain ε11 in both arrangements for different beam thicknesses. The circular arrows show the mechanical moments induced by converse flexoelectricity.

Grahic Jump Location
Fig. 5

Normalized voltage as a function of the normalized beam thickness for the parallel bimorph arrangements: negatively (P) and positively (P+) polarized layers. The results are obtained for the piezoelectric bimorphs with and without flexoelectricity.

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