Collinear and Periodic Electrode-Ceramic Interfacial Cracks in Piezoelectric Bimaterials

2004 ◽  
Vol 71 (4) ◽  
pp. 486-492 ◽  
Author(s):  
Christoph Ha¨usler ◽  
Cun-Fa Gao ◽  
Herbert Balke
Keyword(s):  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Crack Problem ◽  
Interfacial Crack ◽  
Mixed Boundary Conditions ◽  
Interfacial Cracks ◽  
Field Intensity Factors ◽  
Work Done ◽  
Electric Loads ◽  
Relevant Work

Field singularities of collinear and collinear periodic interface cracks between an electrode and a piezoelectric matrix are studied in terms of the Stroh formalism for mixed boundary conditions. In contrast to the relevant work done previously on this subject, the problem is solved based on the assumption that the upper and lower planes embedding the electrode consist of two arbitrary piezoelectric materials, and the cracks are assumed to be permeable. The problem is reduced to an interfacial crack problem equivalent to that in purely elastic media. Explicit expressions are presented for the complex potentials and field intensity factors. All the field variables exhibit oscillatory singularities, and their intensities are dependent on the material properties and the applied mechanical loads, but not on the applied electric loads.

Electrode-Ceramic Interfacial Cracks in Piezoelectric Multilayer Materials

1999 ◽  
Vol 67 (2) ◽  
pp. 255-261 ◽  
Author(s):  
C. Ru
Keyword(s):  
Shear Stress ◽  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Boundary Value ◽  
Practical Interest ◽  
Mixed Boundary Value Problem ◽  
Electrode Layer ◽  
Interfacial Cracks ◽  
Electroelastic Fields

A thin electrode layer embedded at the interface of two piezoelectric materials represents a common feature of many electroceramic multilayer devices. The analysis of interface cracks between the embedded electrode layer and piezoelectric ceramic leads to a nonstandard mixed boundary value problem which likely prevents a general analytical solution. The present work shows that the associated mixed boundary value problem does indeed admit an exact elementary solution for a special case of major practical interest in which the two piezoelectric half-planes are poled in opposite directions perpendicular to the electrode layer. In this case, it is found that oscillatory singularity disappears, in spite of the unsymmetric characters of the problem, and electroelastic fields exhibit power singularities. Particular emphasis is placed on the near-tip singular stresses along the bonded interface. The results show that tensile stress exhibits the square root singularity along the interface whereas shear stress exhibits the dominant-order nonsquare root singularity. In addition, the present model indicates that a pure electric-field loading could induce the dominant-order singular shear stress directly ahead of the interface crack tip. [S0021-8936(00)00602-4]

Dynamic Anti-Plane Characteristic of Two Dissimilar Piezoelectric Media with an Interfacial Crack

2009 ◽  
Vol 417-418 ◽  
pp. 869-872
Author(s):  
Tian Shu Song ◽  
Dong Li ◽  
Tammam Merhej
Keyword(s):  
Stress Intensity ◽  
Dynamic Stress ◽  
Piezoelectric Materials ◽  
Dynamic Stress Intensity Factor ◽  
Interfacial Crack ◽  
Physical Parameters ◽  
Dynamic Stress Intensity Factors ◽  
Piezoelectric Media ◽  
Time Harmonic ◽  
Electric Loads

Dynamic anti-plane characteristic is investigated theoretically on two dissimilar piezoelectric media with an interfacial crack subjected to time-harmonic incident anti-plane shearing in this paper. The formulations are based on the method of complex variable and Green’s function. Dynamic stress intensity factors at the crack’s tip are obtained by solving boundary value problems with the methods of conjunction and crack-division technique. The calculating results are plotted to show how the frequencies of incident wave, all kinds physical parameters of two dissimilar piezoelectric materials, applied electric loads and the dimension of the interfacial crack influence upon the dynamic stress intensity factor (DSIF). And some of the calculating results are compared with other published documents.

scholarly journals Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics

2011 ◽  
Vol 31 (1) ◽  
pp. 65 ◽  
Author(s):  
Dang Quang A ◽  
Mai Xuan Thao
Keyword(s):  
Iterative Method ◽  
Biharmonic Equation ◽  
Numerical Experiments ◽  
Mixed Boundary ◽  
Crack Problem ◽  
Mixed Boundary Conditions ◽  
Airy Stress Function ◽  
Mixed Boundary Value Problem ◽  
Poisson Equations ◽  
Mixed Problems

In this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The convergence of the method is established theoretically and illustrated on many numerical experiments.

scholarly journals Micromechanical modeling of architected piezoelectric foam with simplified boundary conditions for hydrophone applications

2021 ◽  
pp. 1045389X2098391
Author(s):  
Kamran A Khan ◽  
Hamad K Alarafati ◽  
Muhammad Ali Khan
Keyword(s):  
Boundary Conditions ◽  
Elastic Anisotropy ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Micromechanical Model ◽  
Mixed Boundary Conditions ◽  
Analytical Models ◽  
Micromechanical Modeling ◽  
Generation Process ◽  
Porous Microstructures

Architected piezoelectric materials with controlled porosity are of interest for applications such as hydrophones, miniature accelerometers, vibratory sensors, and contact microphones. Current analytical modeling approach cannot be readily applied to design architected periodic piezoelectric foams with tunable properties while exhibiting elastic anisotropy and piezoelectric activity. This study presents micromechanical-finite element (FE) models to characterize the electromechanical properties of architected piezoelectric foams. The microstructure with zero-dimension (3-0 foam, spherical porosity) and one-dimensional (3-1 foam, cylindrical porosity) connectivity were considered to analyze the effect of porosity connectivity on the performance of piezoelectric foam. 3D FE models of the 3-0 and 3-1 foams were developed and using the intrinsic symmetry of porous structures simplified mixed boundary conditions (MBCs) equivalent to periodic boundary conditions (PBC) were proposed. The proposed approach is simple and eliminates the need of tedious mesh generation process on opposite boundary faces on the micromechanical model of porous microstructures with PBCs. The results obtained from the proposed micromechanics-FE models were compared with those obtained by means of the analytical models based on micromechanics theories, and FE models with PBCs reported in the literature for both 3-0 and 3-1 type foams. An excellent agreement was observed. The computed effective elastic, piezoelectric and dielectric properties and corresponding figure of merit (FOM) revealed that piezoelectric foams with 3-0 connectivity exhibit enhanced hydrostatic FOM as compared to piezoelectric foams with 3-1 connectivity. It is concluded that spherical porosity is more suitable to hydrophone applications.

Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

2021 ◽  
pp. 108128652110149
Author(s):  
Ni An ◽  
Tianshu Song ◽  
Gangling Hou
Keyword(s):  
Stress Concentration ◽  
Dynamic Performance ◽  
Crack Problem ◽  
Interfacial Crack ◽  
Elliptical Hole ◽  
Mapping Method ◽  
Dynamic Stress Intensity Factors ◽  
Interfacial Cracks ◽  
Conformal Mapping Method ◽  
Plane Shearing

The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green’s function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability.

Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

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