Analytical studies on Mode III fracture in flexoelectric solids

2021 ◽  
pp. 1-32
Author(s):  
Xinpeng Tian ◽  
Mengkang Xu ◽  
Haiyang Zhou ◽  
Qian Deng ◽  
Qun Li ◽  
...  
Keyword(s):  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Expansion Method ◽  
Gradient Field ◽  
J Integral ◽  
Mode Iii ◽  
Flexoelectric Effect ◽  
Local Strength ◽  
Out Of Plane ◽  
Plane Displacement

Abstract Due to the stress concentration near crack tips, strong flexoelectric effect would be observed there, which might lead to new applications of flexoelectricity in material science and devices. However, different from the flexoelectric effect in cantilever beams or truncated pyramids, at the crack tip, multiple components of strain gradients with nonuniform distribution contribute to the flexoelectric effect, which makes the problem extremely complex. In this paper, with the consideration of both direct and converse flexoelectricity, the electromechanical coupling effect around the tip of a Mode III crack is studied analytically. Based on the Williams' expansion method, the displacement field, polarization field, strain gradient field along with the actual physical stresses field are solved. A path independent J-integral for Mode III cracks in flexoelectric solids is presented. Our results indicate that the existence of flexoelectricity leads to a decrease of both the J-integral and the out-of-plane displacement in Mode III cracks, which means that the flexoelectric effect around the tip of Mode III cracks enhances the local strength of materials.

Distributed Modal Signals of Conical Shells Based on Flexoelectric Effect

2012 ◽  
Author(s):  
H. Li ◽  
S. D. Hu ◽  
H. S. Tzou
Keyword(s):  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Ritz Method ◽  
Strain Component ◽  
Conical Shells ◽  
Total Signal ◽  
Flexoelectric Effect ◽  
Bending Strain ◽  
Spatially Distributed ◽  
Strain Components

Flexoelectricity is known as the electromechanical coupling effect between the strain gradient and the polarization. It is the only contribution of polarization from inhomogeneous mechanical deformation in nonpiezoelectric materials. Conical shells are commonly used as injectors, sprays and rocket nozzles, etc, which are generally clamped at the minor end and free at the major end when mounted. In this study, a flexoelectric layer is laminated on conical shells with clamped-free boundary conditions (BCs) to monitor the natural modal signal distributions. The direct flexoelectric effect defined in a tri-orthogonal coordinate system is presented first, followed by the sensing mechanism of a generic flexoelectric sensor patch. The mode shape functions of conical shells obtained by using the Rayleigh-Ritz method are briefly reviewed. The spatially distributed microscopic sensing signal with respect to position coordinates is evaluated in detail to reveal the modal signal distributions. Due to the gradient effect, the bending strain component is the only contribution to the total sensing signal. The total signal consists of two components resulting from the two bending strain components: circumferential bending strains and longitudinal bending strains. Analytical results show that, the flexoelectric sensing signal induced by the circumferential bending strain is the dominant contribution to the total signal for lower order modes. The optimal location of flexoelectric sensors is discussed for selected vibration modes.

Coupling Effect Analysis of 3D Interior Structural-Acoustic Problems Using Wave Based Method

2011 ◽  
Vol 228-229 ◽  
pp. 526-531
Author(s):  
Cai Xia You ◽  
Guang De Zhang
Keyword(s):  
Arbitrary Shape ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Cavity Depth ◽  
Effect Analysis ◽  
Acoustic Coupling ◽  
Acoustic Cavity ◽  
Prediction Technique ◽  
Out Of Plane ◽  
Plane Displacement

This paper describes the basic concept of the new technique for the modeling of the structural-acoustic coupling between the pressure field in an acoustic cavity with arbitrary shape and the out-of-plane displacement of a flat plate with arbitrary shape. It is illustrated through a three-dimensional validation example that the new prediction technique yields a high accuracy. The effect of the cavity depth and the coupling interface area on the strength of mutual coupling interaction are discussed in detail.

Out-of-Plane Displacement Derivative Measurements Using Interferometric Strain/Slope Gage

1996 ◽  
Vol 63 (4) ◽  
pp. 1033-1038 ◽  
Author(s):  
Keyu Li
Keyword(s):  
Coupling Effect ◽  
Controlled System ◽  
High Deformation ◽  
Out Of Plane ◽  
Computer Controlled ◽  
Fringe Patterns ◽  
Photodiode Arrays ◽  
Plane Displacement ◽  
Deformation Gradients ◽  
Derivatives Of

An optical method originally developed for measuring derivatives of in-plane displacements is redefined to measure derivatives of out-of-plane displacements. The technique is based on interference of laser beams reflected and diffracted from two microindentations closely depressed on a specimen surface. As in-plane and out-of-plane displacements cause the microindentations to move relatively to each other, the two interference fringe patterns change accordingly. Movement of the interference fringes is monitored with linear photodiode arrays and analyzed via a computer-controlled system that allows simultaneous measurements of the in-plane and out-of-plane displacement derivatives. The technique is referred to as the interferometric strain/slope gage (ISSG). Having short gage length (˜100 μm), the technique is unique for measurements of high deformation gradients and for applications in complex geometries. Its principle as well as an experimental validation of measuring bending strains/stresses and deflection slopes in a cantilever beam is presented. The experiment shows that both the first-order and second-order derivatives of out-of-plane displacements can be obtained. Measurement sensitivities to in-plane and out-of-plane rigid-body motions are systematically investigated. The technique can be potentially extended to measure large deflection angles. The derived governing equations indicate a coupling effect between the in-plane and out-of-plane components. The associated instrumentation for data acquisition and analysis is described in great detail.

An hourglass-type electromagnetic isolator with negative resistance electromagnetic shunt circuit

2020 ◽  
Vol 64 (1-4) ◽  
pp. 549-556
Author(s):  
Yajun Luo ◽  
Linwei Ji ◽  
Yahong Zhang ◽  
Minglong Xu ◽  
Xinong Zhang
Keyword(s):  
Vibration Isolation ◽  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Negative Resistance ◽  
Isolation System ◽  
Amplitude Vibration ◽  
Vibration Responses ◽  
The Stability ◽  
Isolation Performance ◽  
Shunt Circuit

The present work proposed an hourglass-type electromagnetic isolator with negative resistance (NR) shunt circuit to achieve the effective suppression of the micro-amplitude vibration response in various advanced instruments and equipment. By innovatively design of combining the displacement amplifier and the NR electromagnetic shunt circuit, the current new type of vibration isolator not only can effectively solve the problem of micro-amplitude vibration control, but also has significant electromechanical coupling effect, to obtain excellent vibration isolation performance. The design of the isolator and motion relationship is presented firstly. The electromechanical coupling dynamic model of the isolator is also given. Moreover, the optimal design of the NR electromagnetic shunt circuit and the stability analysis of the vibration isolation system are carried out. Finally, the simulation results about the transfer function and vibration responses demonstrated that the isolator has a significant isolation performance.

scholarly journals Sensor Integrated Load-Bearing Structures: Measuring Axis Extension with DIC-Based Transducers

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4104
Author(s):  
Nassr Al-Baradoni ◽  
Peter Groche
Keyword(s):  
Cost Effective ◽  
Image Correlation ◽  
Maximum Deviation ◽  
Single Image ◽  
Eccentric Load ◽  
Load Bearing ◽  
Out Of Plane ◽  
Axis Extension ◽  
Plane Displacement ◽  
Imaging Sensor

In this paper we present a novel, cost-effective camera-based multi-axis force/torque sensor concept for integration into metallic load-bearing structures. A two-part pattern consisting of a directly incident and mirrored light beam is projected onto the imaging sensor surface. This allows the capturing of 3D displacements, occurring due to structure deformation under load in a single image. The displacement of defined features in size and position can be accurately analyzed and determined through digital image correlation (DIC). Validation on a prototype shows good accuracy of the measurement and a unique identification of all in- and out-of-plane displacement components under multiaxial load. Measurements show a maximum deviation related to the maximum measured values between 2.5% and 4.8% for uniaxial loads ( and between 2.5% and 10.43% for combined bending, torsion and axial load. In the course of the investigations, the measurement inaccuracy was partly attributed to the joint used between the sensor parts and the structure as well as to eccentric load.

scholarly journals Locally Corroded Stiffener Effect on Shear Buckling Behaviors of Web Panel in the Plate Girder

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Jungwon Huh ◽  
In-Tae Kim ◽  
Jin-Hee Ahn
Keyword(s):  
Corrosion Damage ◽  
Element Analysis ◽  
Buckling Strength ◽  
Lower Shear ◽  
Out Of Plane ◽  
Shear Buckling ◽  
Buckling Failure ◽  
Plane Displacement ◽  
The Web ◽  
Plate Girder

The shear buckling failure and strength of a web panel stiffened by stiffeners with corrosion damage were examined according to the degree of corrosion of the stiffeners, using the finite element analysis method. For this purpose, a plate girder with a four-panel web girder stiffened by vertical and longitudinal stiffeners was selected, and its deformable behaviors and the principal stress distribution of the web panel at the shear buckling strength of the web were compared after their post-shear buckling behaviors, as well as their out-of-plane displacement, to evaluate the effect of the stiffener in the web panel on the shear buckling failure. Their critical shear buckling load and shear buckling strength were also examined. The FE analyses showed that their typical shear buckling failures were affected by the structural relationship between the web panel and each stiffener in the plate girder, to resist shear buckling of the web panel. Their critical shear buckling loads decreased from 82% to 59%, and their shear buckling strength decreased from 88% to 76%, due to the effect of corrosion of the stiffeners on their shear buckling behavior. Thus, especially in cases with over 40% corrosion damage of the vertical stiffener, they can have lower shear buckling strength than their design level.

Mechanism of the Transition From In-Plane Buckling to Helical Buckling for a Stiff Nanowire on an Elastomeric Substrate

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Youlong Chen ◽  
Yong Zhu ◽  
Xi Chen ◽  
Yilun Liu
Keyword(s):  
High Performance ◽  
Three Dimensional ◽  
Stretchable Electronics ◽  
Buckling Mode ◽  
Design And Optimization ◽  
Out Of Plane ◽  
Plane Direction ◽  
Plane Displacement ◽  
Helical Buckling ◽  
Selection Of

In this work, the compressive buckling of a nanowire partially bonded to an elastomeric substrate is studied via finite-element method (FEM) simulations and experiments. The buckling profile of the nanowire can be divided into three regimes, i.e., the in-plane buckling, the disordered buckling in the out-of-plane direction, and the helical buckling, depending on the constraint density between the nanowire and the substrate. The selection of the buckling mode depends on the ratio d/h, where d is the distance between adjacent constraint points and h is the helical buckling spacing of a perfectly bonded nanowire. For d/h > 0.5, buckling is in-plane with wavelength λ = 2d. For 0.27 < d/h < 0.5, buckling is disordered with irregular out-of-plane displacement. While, for d/h < 0.27, buckling is helical and the buckling spacing gradually approaches to the theoretical value of a perfectly bonded nanowire. Generally, the in-plane buckling induces smaller strain in the nanowire, but consumes the largest space. Whereas the helical mode induces moderate strain in the nanowire, but takes the smallest space. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and three-dimensional complex nanostructures.

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.

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