Size-Dependent Flexoelectric Response of a Truncated Cone and the Consequent Ramifications for the Experimental Measurement of Flexoelectric Properties

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Qian Deng
Keyword(s):  
Scale Effects ◽  
Piezoelectric Materials ◽  
Electrical Response ◽  
Electric Polarization ◽  
Strain Gradients ◽  
Size Dependent ◽  
Flexoelectric Effect ◽  
Truncated Cone ◽  
Shape Effects ◽  
Typical Model

The flexoelectric effect is an electromechanical phenomenon that is universally present in all dielectrics and exhibits a strong size-dependency. Through a judicious exploitation of scale effects and symmetry, flexoelectricity has been used to design novel types of structures and materials including piezoelectric materials without using piezoelectric. Flexoelectricity links electric polarization with strain gradients and is rather difficult to estimate experimentally. One well-acknowledged approach is to fabricate truncated pyramids and/or cones and examine their electrical response. A theoretical model is then used to relate the measured experimental response to estimate the flexoelectric properties. In this work, we revisit the typical model that is used in the literature and solve the problem of a truncated cone under compression or tension. We obtained closed-form analytical solutions to this problem and examine the size and shape effects of flexoelectric response of the aforementioned structure. In particular, we emphasize the regime in which the existing models are likely to incur significant error.

scholarly journals Conservation Integrals in Nonhomogeneous Materials with Flexoelectricity

2021 ◽  
Vol 11 (2) ◽  
pp. 681
Author(s):  
Pengfei Yu ◽  
Weifeng Leng ◽  
Yaohong Suo
Keyword(s):  
Electromechanical Coupling ◽  
Energy Momentum Tensor ◽  
Great Influence ◽  
Operator Method ◽  
Electric Polarization ◽  
Momentum Tensor ◽  
Noether Theorem ◽  
Strain Gradients ◽  
Flexoelectric Effect ◽  
Nonhomogeneous Materials

The flexoelectricity, which is a new electromechanical coupling phenomenon between strain gradients and electric polarization, has a great influence on the fracture analysis of flexoelectric solids due to the large gradients near the cracks. On the other hand, although the flexoelectricity has been extensively investigated in recent decades, the study on flexoelectricity in nonhomogeneous materials is still rare, especially the fracture problems. Therefore, in this manuscript, the conservation integrals for nonhomogeneous flexoelectric materials are obtained to solve the fracture problem. Application of operators such as grad, div, and curl to electric Gibbs free energy and internal energy, the energy-momentum tensor, angular momentum tensor, and dilatation flux can also be derived. We examine the correctness of the conservation integrals by comparing with the previous work and discuss the operator method here and Noether theorem in the previous work. Finally, considering the flexoelectric effect, a nonhomogeneous beam problem with crack is solved to show the application of the conservation integrals.

A Study of the Flexoelectric Effect on the Electroelastic Fields of a Cantilevered Piezoelectric Nanoplate

2017 ◽  
Vol 09 (04) ◽  
pp. 1750056 ◽  
Author(s):  
Xining Wang ◽  
Rui Zhang ◽  
Liying Jiang
Keyword(s):  
Boundary Conditions ◽  
Electromechanical Coupling ◽  
Piezoelectric Materials ◽  
Governing Equations ◽  
Size Dependent ◽  
Flexoelectric Effect ◽  
Electroelastic Fields ◽  
Geometric Ratio ◽  
Electrical Loads ◽  
Kirchhoff Plate Model

Flexoelectricity, a spontaneous polarization in linear response to strain gradients or non-uniform deformation, is believed to contribute to the size-dependent electromechanical coupling of piezoelectric materials at the nanoscale. In the current work, the flexoelectric effect upon the static bending behaviors of a cantilevered piezoelectric nanoplate (PNP) is studied. Based on the Kirchhoff plate model and the extended linear piezoelectric theory, the non-conventional governing equations and the boundary conditions of the PNP under both mechanical and electrical loads are derived with the incorporation of the flexoelectric effect. Finite difference method (FDM) is performed to get the numerical solution for the electroelastic fields of the plate. Simulation results show that the flexoelectric effect is more prominent for the thinner plates with smaller thickness. It is also found that the flexoelectric effect upon the electroelastic responses of the clamped PNP is also sensitive to some other factors, including the boundary conditions, the plate geometric ratio, and the applied mechanical and electrical loads. This work aims to provide an increased understanding of the size-dependent electromechanical coupling properties of a piezoelectric plate structure.

FLEXOELECTRIC COMPOSITE — A NEW PROSPECT FOR LEAD-FREE PIEZOELECTRICS

2010 ◽  
Vol 03 (01) ◽  
pp. 79-81 ◽  
Author(s):  
BAOJIN CHU ◽  
WENYI ZHU ◽  
NAN LI ◽  
L. ERIC CROSS
Keyword(s):  
Piezoelectric Properties ◽  
Piezoelectric Materials ◽  
Physical Phenomenon ◽  
Mechanical Strain ◽  
Dielectric Materials ◽  
Electric Polarization ◽  
Lead Free ◽  
Piezoelectric Response ◽  
Bst Ceramics ◽  
Better Than

Flexoelectricity describes the physical phenomenon of the generation of electric polarization from mechanical strain gradient in solid insulators. In common dielectric materials, the flexoelectric coefficient is trivially small ~10-10 C/m. In Ba(Sr,Ti)O 3 (BST) ceramics, flexoelectric coefficient up to 10-4 C/m was observed. Such high coefficient makes it possible to design high piezoelectric response flexoelectric composites. In this letter, we will demonstrate that the newly designed flexoelectric composites could have piezoelectric properties better than conventional piezoelectric materials.

scholarly journals Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1935 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev ◽  
Krzysztof Kamil Żur
Keyword(s):  
Material Properties ◽  
Gradient Elasticity ◽  
Small Scale ◽  
Stability Equation ◽  
Strain Gradients ◽  
Size Dependent ◽  
Different Types ◽  
Dependent Property ◽  
The Stability ◽  
Transverse Deflection

We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant.

Sensing Signal and Energy Generation Analysis on a Flexoelectric Beam

2012 ◽  
Author(s):  
S. D. Hu ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Cantilever Beam ◽  
Coupling Effect ◽  
Mechanical Strain ◽  
Electric Energy ◽  
Energy Generation ◽  
Electric Polarization ◽  
Ambient Vibration ◽  
Electric Voltage ◽  
Flexoelectric Effect ◽  
Fourth Mode

Flexoelectricity is known as an electromechanical gradient coupling effect. The direct flexoelectric effect that can convert mechanical strain gradient into electric polarization (or electric field) plays an important role in charge generation in the situation when piezoelectricity is absent. This study focuses on the application of the direct flexoelectric effect based on a flexoelectric cantilever beam to investigate its effectiveness of sensing signal and energy generation. The dielectric cantilever beam is deposited with electrodes both on top and bottom surfaces to generate an electric voltage. The sensing mechanism of flexo-piezo-electric effect is analyzed and the expression of sensing signal is derived. Results show that the output sensing signal is only contributed by the flexoelectric effect while the piezoelectric effect is eliminated due to the symmetric bending strains through the beam thickness. The spatial distribution of sensing signal when the fully covered electrode is uniformly segmented to 10 patches is evaluated as an illustration, and the flexoelectric sensitivity of about 0.15V/mm for the first mode and 4V/mm for the fourth mode is achieved. The optimal sensing position is dependent of the electrode size and the vibration mode and in general, it locates where the difference between the slopes at two ends of the electrode patch reaches maximum. Based on the flexoelectric voltage, the energy generation power is also conducted when the flexoelectric cantilever beam is treated as distributed energy harvesters. As a result, the maximal power of RMS is about 1.5×10−8W/mm for the first mode and increases to about 0.6mW/mm for the fourth mode. It provides an alternative way to harvest electric energy from the ambient vibration without using piezoelectricity.

On strain gradients and size-dependent hardening descriptions in crystal plasticity frameworks

2006 ◽  
Vol 12 (5) ◽  
pp. 407-411 ◽  
Author(s):  
Chung -Souk Han ◽  
Franz Roters ◽  
Dierk Raabe
Keyword(s):  
Crystal Plasticity ◽  
Strain Gradients ◽  
Size Dependent

Distributed flexoelectric modal signals on circular cylindrical shells

2017 ◽  
Vol 232 (6) ◽  
pp. 952-961 ◽  
Author(s):  
Hua Li ◽  
Kaiming Hu ◽  
HS Tzou
Keyword(s):  
Strain Gradient ◽  
Cylindrical Shells ◽  
Mechanical Strain ◽  
Electric Polarization ◽  
Design Parameters ◽  
Flexoelectric Effect ◽  
Bending Strain ◽  
Longitudinal Bending ◽  
Circular Cylindrical Shells ◽  
Sensing Characteristics

Flexoelectricity exhibits both direct effect and converse effect. For direct flexoelectric effect, mechanical strain gradients induce a homogeneous electric polarization in dielectrics. Thus, the induced electric field between the electrodes can be measured. Compared with the piezoelectric sensors, the main advantage of the flexoelectric sensors is that they are not sensitive to the in-plane strains. This paper presents segmented flexoelectric sensors laminated on circular cylindrical shells, and investigates the electromechanical strain-gradient/signal-generation characteristics and distributed modal flexoelectric signals on the cylindrical shells. The dynamic equations of the proposed flexoelectric sensor are derived based on the direct flexoelectric effect and thin shell assumptions. The model of modal signal is derived to investigate the sensing characteristics. In case studies, the effects of design parameters, i.e. size and thickness of the sensors and geometry of the shells, are evaluated and compared. Numerical results indicate that the contribution of longitudinal bending strain gradient is dominant in the total signals of most evaluated modes, except that in modes 1 and 2, where the contribution of the circumferential bending strain gradient is slightly higher. The amplitudes of the modal signals decrease with the shell radius, but increase with the sensor thickness.

Nonlinear Pull-In Instability of Strain Gradient Microplates Made of Functionally Graded Materials

2019 ◽  
Vol 19 (02) ◽  
pp. 1950007 ◽  
Author(s):  
R. Gholami ◽  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Functionally Graded Materials ◽  
Strain Gradient ◽  
Scale Effects ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Graded Materials ◽  
First Order ◽  
Size Dependent

In this paper, the size-dependent nonlinear pull-in behavior of rectangular microplates made from functionally graded materials (FGMs) subjected to electrostatic actuation is numerically studied using a novel approach. The small scale effects are taken into account according to Mindlin’s first-order strain gradient theory (SGT). The plate model is formulated based on the first-order shear deformation theory (FSDT) using the virtual work principle. The size-dependent relations are derived in general form, which can be reduced to those based on different elasticity theories, including the modified strain gradient, modified couple stress and classical theories (MSGT, MCST and CT). The solution of the problem is arrived at by employing an efficient matrix-based method called the variational differential quadrature (VDQ). First, the quadratic form of the energy functional including the size effects is obtained. Then, it is discretized by the VDQ method using a set of matrix differential and integral operators. Finally, the achieved discretized nonlinear equations are solved by the pseudo arc-length continuation method. In the numerical results, the effects of material length scale parameters, side length-to-thickness ratio and FGM’s material gradient index on the nonlinear pull-in instability of microplates with different boundary conditions are investigated. A comparison is also made between the predictions by the MSGT, MCST and CT.

scholarly journals Large Piezoelectric Response and Ferroelectricity in Li and V/Nb/Ta co-doped w-AlN

2020 ◽  
Author(s):  
Mohammad Noor-A-Alam ◽  
Oskar Olszewski ◽  
Humberto Campanella ◽  
Michael Nolan
Keyword(s):  
Acoustic Wave ◽  
Density Functional ◽  
Electromechanical Coupling ◽  
Piezoelectric Materials ◽  
Electric Polarization ◽  
Piezoelectric Response ◽  
Co Doping ◽  
Piezoelectric Strain ◽  
Co Doped ◽  
Piezoelectric Strain Constant

<div>Based on density functional theory, we show that Li and</div><div>X (X=V, Nb and Ta) co-doping in 1Li:1X ratio broadens the</div><div>compositional freedom for significant piezoelectric enhancement in w-AlN, promising them to be good alternatives of expensive Sc. Interestingly, these co-doped w-AlN also show quite large spontaneous electric polarization about 0.80 C/m2 with the possibility of ferroelectric polarization switching, opening new possibilities in wurtzite nitrides. Increase in piezoelectric stress constant (e33) with decrease in elastic constant ( C33 ) results enhancement in piezoelectric strain constant ( d33 ), which is desired for improving the performance of resonators for high frequency RF signals. Also, these co-doped w-AlN are potential lead-free piezoelectric materials for energy harvesting and sensors as they improve the longitudinal electromechanical coupling constant (K^2 33), transverse piezoelectric strain constant (d31), and figure of merit for power generation. However, the enhancement in K^2 33 is not as pronounced as that in d33, because co-doping increases the dielectric constant. The longitudinal acoustic wave velocity (7.09 km/s) of Li0.1875Ta0.1875Al0.625N is quite comparable with that of commercially used piezoelectric LiNbO3 or LiTaO3 in special cuts (about 5~7 km/s) despite the fact that the acoustic wave velocities drop with co-doping or Sc concentration.</div>

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