scholarly journals Exact Solution for an Anti-Plane Interface Crack between Two Dissimilar Magneto-Electro-Elastic Half-Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Bogdan Rogowski
Keyword(s):  
Magnetic Induction ◽  
Electric Displacement ◽  
Dual Integral Equations ◽  
Crack Face ◽  
Poling Direction ◽  
Electric And Magnetic Fields ◽  
Crack Tips ◽  
Square Root Singularity ◽  
Field Intensity Factors ◽  
Magnetic Potentials

This paper investigated the fracture behaviour of a piezo-electro-magneto-elastic medium subjected to electro-magneto-mechanical loads. The bimaterial medium contains a crack which lies at interface and is parallel to their poling direction. Fourier transform technique is used to reduce the problem to three pairs of dual integral equations. These equations are solved exactly. The semipermeable crack-face magneto-electric boundary conditions are utilized. Field intensity factors of stress, electric displacement, magnetic induction, cracks displacement, electric and magnetic potentials, and the energy release rate are determined. The electric displacement and magnetic induction of crack interior are discussed. Obtained results indicate that the stress field and electric and magnetic fields near the crack tips exhibit square-root singularity.

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.

Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear cracks in piezoelectric media

2021 ◽  
Vol 13 (4) ◽  
pp. 177-195
Author(s):  
Sandeep Singh ◽  
Kuldeep Sharma
Keyword(s):  
Analytical Solutions ◽  
Complex Potential ◽  
Crack Opening ◽  
Electric Displacement ◽  
Potential Functions ◽  
Collinear Cracks ◽  
Crack Face ◽  
Piezoelectric Media ◽  
Fracture Parameters ◽  
Poling Direction

The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters.

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.

scholarly journals Analysis of Mode I Conducting Crack in Piezo-Electro-Magneto-Elastic Layer

2013 ◽  
Vol 18 (1) ◽  
pp. 153-176
Author(s):  
B. Rogowski
Keyword(s):  
Boundary Conditions ◽  
Electric Displacement ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Intensity Factors ◽  
Permeable Crack ◽  
Crack Face ◽  
Field Intensity Factors ◽  
Dielectric Crack ◽  
Thickness Field

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

scholarly journals Nonuniformly Loaded Stack of Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
G. E. Tupholme
Keyword(s):  
Electric Displacement ◽  
Polar Angle ◽  
Antiplane Shear ◽  
Shear Cracks ◽  
Intensity Factors ◽  
One Dimensional ◽  
Isotropic Solid ◽  
Special Cases ◽  
Field Intensity Factors ◽  
Explicit Representations

Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed.

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.

Three-Dimensional Electroelastic Analysis of a Piezoelectric Material With a Penny-Shaped Dielectric Crack

2004 ◽  
Vol 71 (6) ◽  
pp. 866-878 ◽  
Author(s):  
Xian-Fang Li ◽  
Kang Yong Lee
Keyword(s):  
Boundary Conditions ◽  
Piezoelectric Material ◽  
Field Intensity ◽  
Three Dimensional ◽  
Intensity Factors ◽  
Elementary Functions ◽  
Dual Integral Equations ◽  
Electroelastic Field ◽  
Field Intensity Factors ◽  
Dielectric Crack

Previous studies assumed that a crack is either impermeable or permeable, which are actually two limiting cases of a dielectric crack. This paper considers the electroelastic problem of a three-dimensional transversely isotropic piezoelectric material with a penny-shaped dielectric crack perpendicular to the poling axis. Using electric boundary conditions controlled by the boundaries of an opening crack, the electric displacements at the crack surfaces are determined. The Hankel transform technique is employed to reduce the considered problem to dual integral equations. By solving resulting equations, the results are presented for the case of remote uniform loading, and explicit expressions for the electroelastic field at any point in the entire piezoelectric body are given in terms of elementary functions. Moreover, the distribution of asymptotic field around the crack front and field intensity factors are determined. Numerical results for a cracked PZT-5H ceramic are evaluated to examine the influence of the dielectric permittivity of the crack interior on the field intensity factors, indicating that the electric boundary conditions at the crack surfaces play an important role in determining electroelastic field induced by a crack, and that the results are overestimated for an impermeable crack, and underestimated for a permeable crack.

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.

Frictional Indentation of Anisotropic Magneto-Electro-Elastic Materials by a Rigid Indenter

2014 ◽  
Vol 81 (7) ◽  
Author(s):  
Yue-Ting Zhou ◽  
Zheng Zhong
Keyword(s):  
Friction Coefficient ◽  
Plane Stress ◽  
Magnetic Induction ◽  
Volume Fraction ◽  
Mixed Boundary ◽  
Electric Displacement ◽  
Leading Edge ◽  
Singular Integral Equations ◽  
Elastic Materials ◽  
Electrical Displacement

An exact analysis on frictional contact between a rigid punch and anisotropic magneto-electro-elastic materials is performed, within the framework of the fully coupled theory. The indenter moves relative to magneto-electro-elastic materials, and Coulomb friction law is used. The mixed boundary value problem is reduced to singular integral equations of the second kind with analytical solution presented. For a triangular or semiparabolic indenter, explicit expression for surface physical in-plane stress, electrical displacement and magnetic induction are obtained. Influences of the friction coefficient and the volume fraction on contact behaviors are detailed under the prescribed contact loading conditions. Under either a triangular or semiparabolic indenter, the surface in-plane stress, electric displacement and magnetic induction are discontinuous and unbounded around the leading edge, and such a serious near-edge response can be relieved through adjusting the values of the friction coefficient or the volume fraction.

Anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable regular triangle nano-hole in magnetoelectroelastic materials

2020 ◽  
pp. 2150127
Author(s):  
Dongsheng Yang ◽  
Guanting Liu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Release Rate ◽  
Magnetic Induction ◽  
Surface Effect ◽  
Electric Displacement ◽  
Magnetoelectroelastic Materials ◽  
Electric Displacement Intensity Factor ◽  
Magnetic Induction Intensity

Based on the Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable triangle nano-hole in magnetoelectroelastic materials with surface effect is studied. The exact solutions of the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate are obtained under the boundary conditions of magnetoelectrically permeable and impermeable. The numerical examples show the influence of surface effect on the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate under two different boundary conditions. It can be seen that the surface effect leads to the coupling of stress, electric and magnetic field, and with the increase of cavity size, the influence of surface effect begins to decrease until it tends to classical elasticity theory.

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