Dynamic analysis of two collinear permeable Mode-I cracks in piezoelectric materials based on non-local piezoelectricity theory

2019 ◽  
Vol 15 (6) ◽  
pp. 1274-1293
Author(s):  
Haitao Liu ◽  
Shuai Zhu
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Local Stress ◽  
Classical Solutions ◽  
Mode I ◽  
Dual Integral Equations ◽  
Content Type ◽  
Present Solution ◽  
Crack Tips ◽  
Non Local

Purpose Based on the non-local piezoelectricity theory, this paper is concerned with two collinear permeable Mode-I cracks in piezoelectric materials subjected to the harmonic stress wave. The paper aims to discuss this issue. Design/methodology/approach According to the Fourier transformation, the problem is formulated into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. Findings Finally, the dynamic non-local stress and the dynamic non-local electric displacement fields near the crack tips are obtained. Numerical results are provided to illustrate the effects of the distance between the two collinear cracks, the lattice parameter and the circular frequency of the incident waves on the entire dynamic fields near the crack tips, which play an important role in designing new structures in engineering. Originality/value Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack tips in piezoelectric materials. It is found that the maximum stress and maximum electric displacement can be used as a fracture criterion.

Fundamental solutions of two 3D rectangular semi-permeable cracks in transversely isotropic piezoelectric media based on the non-local theory

2020 ◽  
Vol 16 (6) ◽  
pp. 1497-1520
Author(s):  
Haitao Liu ◽  
Liang Wang
Keyword(s):  
Electric Displacement ◽  
Transversely Isotropic ◽  
Elastic Behavior ◽  
Classical Solutions ◽  
Local Theory ◽  
Dual Integral Equations ◽  
Piezoelectric Media ◽  
Content Type ◽  
Present Solution ◽  
Non Local

PurposeThe paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.Design/methodology/approachThe fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.FindingsDifferent from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.Originality/valueAccording to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

Basic solution of two collinear mode-I cracks in the orthotropic medium by use of the non-local theory

2017 ◽  
Vol 13 (1) ◽  
pp. 100-115 ◽  
Author(s):  
Haitao Liu
Keyword(s):  
Stress Singularity ◽  
Local Theory ◽  
Mode I ◽  
Basic Solution ◽  
Orthotropic Medium ◽  
Dual Integral Equations ◽  
Content Type ◽  
Present Solution ◽  
Crack Tips ◽  
Non Local

Purpose The purpose of this paper is to present the basic solution of two collinear mode-I cracks in the orthotropic medium by the use of the non-local theory. Design/methodology/approach Meanwhile, the generalized Almansi’s theorem and the Schmidt method are used. By the Fourier transform, it is converted to a pair of dual integral equations. Findings Numerical examples are provided to show the effects of the crack length, the distance between the two collinear cracks and the lattice parameter on the stress field near the crack tips in the orthotropic medium. Originality/value The present solution exhibits no stress singularity at the crack tips in the orthotropic medium.

Dynamic non-local stress analysis of two collinear semi-permeable mode-I cracks in a piezoelectric medium

2019 ◽  
Vol 30 (20) ◽  
pp. 3100-3112
Author(s):  
Hai-Tao Liu ◽  
Wen-Juan Wu ◽  
Jian-Guo Wu
Keyword(s):  
Dynamic Stress ◽  
Electric Displacement ◽  
Local Stress ◽  
Lattice Parameter ◽  
Piezoelectric Medium ◽  
Mode I ◽  
Collinear Cracks ◽  
Dual Integral Equations ◽  
Crack Tips ◽  
Non Local

This article investigates the dynamic non-local stress analysis of two collinear semi-permeable mode-I cracks in a piezoelectric medium under the harmonic waves by using the generalized Almansi theorem and the Schmidt method. Based on the Fourier transform technique, this problem is formulated into coupled dual integral equations. The dynamic stress and the dynamic electric displacement fields at the crack tips are obtained by solving the derived dual integral equations. Numerical examples are provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity of the air inside the crack, and the characteristics of the harmonic wave on the dynamic stress field and the dynamic electric displacement field near the crack tips. The dynamic stress and electric displacement decrease with increasing the distance between two collinear cracks and lattice parameter in a piezoelectric medium. Meanwhile, the dynamic field will impede or enhance crack propagation in piezoelectric medium depending on the circular frequency of the incident wave. Different from the classical solutions, the present solutions exhibit no stress and electric displacement singularities at the crack tips. This work is expected to be helpful for theoretical modeling of piezoelectric medium at nanoscale.

Scattering of anti-plane shear waves by an interface crack between two bonded dissimilar functionally graded piezoelectric materials

2009 ◽  
Vol 465 (2104) ◽  
pp. 1249-1269 ◽  
Author(s):  
B.M Singh ◽  
J Rokne ◽  
R.S Dhaliwal ◽  
J Vrbik
Keyword(s):  
Integral Equations ◽  
Integral Transform ◽  
Piezoelectric Materials ◽  
Mass Density ◽  
Electric Displacement ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

In the present paper, the dynamic behaviour of a Griffith crack situated at the interface of two bonded dissimilar functionally graded piezoelectric materials (FGPMs) is considered. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPMs vary continuously as an exponential function of the x and y coordinates, and that the FGPMs are under anti-plane mechanical loading and in-plane electrical loading. By using an integral transform technique the problem is reduced to four pairs of dual integral equations, which are transformed into four simultaneous Fredholm integral equations with four unknown functions. By solving the four simultaneous Fredholm integral equations numerically the effects of the material properties on the stress and electric displacement intensity factors are calculated and displayed graphically.

The Non-Local Theory Solution of a Crack in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves

2007 ◽  
Vol 353-358 ◽  
pp. 258-262
Author(s):  
Zhen Gong Zhou ◽  
Lin Zhi Wu
Keyword(s):  
Shear Stress ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Stress Waves ◽  
Functionally Graded ◽  
Local Theory ◽  
Plane Shear ◽  
Functionally Graded Piezoelectric Materials ◽  
Non Local ◽  
Functionally Graded Piezoelectric

In this paper, the non-local theory of elasticity was applied to obtain the dynamic behavior of a Griffith crack in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves. The problem can be solved with the help of a pair of dual integral equations. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips, thus allows us to use the maximum stress as a fracture criterion.

Interaction between a Rigid Cylinder with a Piezoelectric Half-Space with Partial Adhesion

2008 ◽  
Vol 33-37 ◽  
pp. 333-338 ◽  
Author(s):  
Zuo Rong Chen ◽  
Shou Wen Yu
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Contact Region ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Dual Integral Equations ◽  
Slip Region

An axisymmetric problem of interaction of a rigid rotating flat ended punch with a transversely isotropic linear piezoelectric half-space is considered. The contact zone consists of an inner circular adhesion region surrounded by an outer annular slip region with Coulomb friction. Beyond the contact region, the surface of the piezoelectric half-space is free from load. With the aid of the Hankel integral transform, this mixed boundary value problem is formulated as a system of dual integral equations. By solving the dual integral equations, analytical expressions for the tangential stress and displacement, and normal electric displacement on the surface of the piezoelectric half-space are obtained. An explicit relationship between the radius of the adhesion region, the angle of the rotation of the punch, material parameters, and the applied loads is presented. The obtained results are useful for characterization of piezoelectric materials by micro-indentation and micro-friction techniques.

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