Non-local theory solution for a Mode I crack in piezoelectric materials

Zhou, Zhen-Gong; Wu, Linzhi; Du, Shiyu

doi:10.1016/j.euromechsol.2005.10.003

Cited by 45 publications

(42 citation statements)

References 21 publications

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“…Thus, following the manipulations done by Zhou et al [11] via the principle of superposition, the above crack problem can be reduced to the following triple integral equation …”

Section: Basic Formalisms For the Crack Problem In Non-local Piezoelementioning

confidence: 99%

“…1. A generalized plane strain problem in transversely isotropic piezoelectric materials is considered, where there only exist nine material constants: c 11 , c 13 , c 33 , c 44 , e 15 , e 13 , e 33 , χ 11 and χ 33 (in Viogt's notation). The cracked piezoelectric body is subjected to the remote combined mechanical and electrical loadings denoted by σ ∞ 21 , σ ∞ 22 and D ∞ 2 , respectively.…”

Section: Basic Formalisms For the Crack Problem In Non-local Piezoelementioning

confidence: 99%

“…The non-local piezoelectric material constants can be determined by comparing the dispersion of perfect crystal lattices with those of plane waves in the non-local theory [11,13] …”

Section: Basic Formalisms For the Crack Problem In Non-local Piezoelementioning

confidence: 99%

“…And thus other researchers are motivated to explore other theoretical ways different from the classical PLFM. For example, Zhou et al [11], Zhou and Wang [12] and Zhou et al [13] extended the non-local theory firstly proposed by Eringen et al [14] for the isotropic elastic material to treat the semi-permeable crack in piezoelectric materials. Unlike the classical LPFM, the non-local theory yields finite stresses and electric displacement near the crack tip.…”

Section: Introductionmentioning

confidence: 96%

“…Recently, Zhou et al [11] studied the semi-permeable crack in non-local piezoelectric materials subjected to a simple tension loading. By means of the Fourier transform, the problem can be solved via two pair of dual integral equations.…”

Section: Introductionmentioning

confidence: 99%

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Investigation of the crack problem in non-local piezoelectric materials under combined electromechanical loadings

Chen

2008

Acta Mech Sin

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The present investigation of the crack problem in piezoelectric materials is performed based on the non-local theory. After some manipulations, the impermeable crack, the permeable crack (the crack gap is full of NaCI solution), and the semi-permeable crack (the crack gap is full of air or silicon oil) are reduced to a uniform formulation by assuming the normal electric displacement on the crack surfaces to be an unknown variable. Thus, a triple integral equation with the unknown normal electric displacement is established. By using the Newton iterative method and solving the triple integral equation, it is found that the normal electric displacement on the crack surfaces is no longer a constant as determined by previous studies, rather, it depends upon the remote combined electromechanical loadings. Numerical results of the stresses and electric displacement fields show that there are no singularities at the crack tips so that the stresses remain finite. It is of great significance that the concrete electric boundary condition on the crack surfaces exerts significant influence on the near-tip fields and in this way plays an important role in evaluating the crack stability in the non-local piezoelectric materials. More specifically, the impermeable crack model always overestimates the finite stresses at the crack tips, whereas the permeable crack model always underestimates them.

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“…Thus, following the manipulations done by Zhou et al [11] via the principle of superposition, the above crack problem can be reduced to the following triple integral equation …”

Section: Basic Formalisms For the Crack Problem In Non-local Piezoelementioning

confidence: 99%

Section: Basic Formalisms For the Crack Problem In Non-local Piezoelementioning

confidence: 99%

“…The non-local piezoelectric material constants can be determined by comparing the dispersion of perfect crystal lattices with those of plane waves in the non-local theory [11,13] …”

Section: Basic Formalisms For the Crack Problem In Non-local Piezoelementioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Investigation of the crack problem in non-local piezoelectric materials under combined electromechanical loadings

Chen

2008

Acta Mech Sin

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Non‐local theory solution of a limited‐permeable mode‐I crack in a piezoelectric/piezomagnetic material plane

Zhou

Zhang

2010

Z Angew Math Mech

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The non‐local theory solution of a limited‐permeable mode‐I crack in a piezoelectric/piezomagnetic media was given by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the lattice parameter, the crack length, the electric permittivity, and the magnetic permeability of the air inside the crack on the stress field, the electric displacement field, and the magnetic field near the crack tip. Different from the classical solution that the present solution exhibits no stress, electric displacement, and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic media.

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Dynamic non‐local theory stress analysis of two equal and collinear mode‐I cracks in the orthotropic medium

Liu

2018

Z Angew Math Mech

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In this study, dynamic stress analysis of two equal and collinear mode‐I cracks in the orthotropic medium is conducted using the non‐local theory, the generalized Almansi's theorem and the Schmidt method. Fourier transform is applied to solve the problem, and the problem is converted to a pair of dual integral equations. The dynamic non‐local stress fields near the crack tips are obtained. The effects of the distance between the two equal and collinear cracks, the circular frequency of the incident waves the lattice parameter on the stress field near the crack tips are discussed. The present solution exhibits no stress singularity at the crack tips in the orthotropic medium, i.e. the dynamic non‐local stress field near the crack tips is finite. The obtained results play an important role in designing new composite structures in engineering.

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Non-local theory solution for a Mode I crack in piezoelectric materials

Cited by 45 publications

References 21 publications

Investigation of the crack problem in non-local piezoelectric materials under combined electromechanical loadings

Investigation of the crack problem in non-local piezoelectric materials under combined electromechanical loadings

Non‐local theory solution of a limited‐permeable mode‐I crack in a piezoelectric/piezomagnetic material plane

Dynamic non‐local theory stress analysis of two equal and collinear mode‐I cracks in the orthotropic medium

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