Transient analysis of multiple interface cracks between two dissimilar functionally graded magneto-electro-elastic layers

Milan, Amir G.; Ayatollahi, M.

doi:10.1007/s00419-020-01699-y

Cited by 11 publications

(7 citation statements)

References 22 publications

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“…Laplace operator. To facilitate the solution of the above equations, it is convenient to use the following definitions 22 :…”

Section: Problem Statementmentioning

confidence: 99%

“…The details of the derivation of Equation 26are not given here. The stress, electric, and magnetic induction intensity factors at the tips of a crack may be defined and evaluated in the Laplace transform domain as follows 22 :…”

Section: Derivation Of the Integral Equations For Multiple Cracks Pro...mentioning

confidence: 99%

“…[15][16][17][18][19][20] The transient fracture problem of piezoelectric-piezomagnetic sandwich structures under the combined anti-plane mechanical and in-plane electrical impacts was investigated by Zhao et al 21 Transient analysis of two bonded functionally graded magneto-electro-elastic layers with multiple interfacial cracks was analyzed by Milan and Ayatollahi. 22 The transient response of multiple impermeable cracks in a piezoelectric layer bonded to an orthotropic layer under anti-plane mechanical and in-plane electrical impact loads was obtained by Ayatollahi et al 23 According to our knowledge, although crack problems in MEEM or FGMEE layer have been investigated by many researchers, the transient analysis of multiple embedded cracks in the FGMEE layer bonded between two orthotropic layers under impact loads has not been investigated. Therefore, this has prompted the undertaking of the present work.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic response of cracked non‐homogeneous magneto‐electro‐elastic layer sandwiched by two dissimilar orthotropic layers

Arhani

Ayatollahi

2022

Fatigue Fract Eng Mat Struct

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This paper is concerned with the transient response of cracked functionally graded magneto-electro-elastic layer (FGMEE) bonded between dissimilar orthotropic layers under impacts. Fourier and Laplace transforms are employed to obtain the analytical solution of a dynamic magneto-electroelastic dislocation with time-dependent Burgers' vector at the FGMEE layer. Expressions for stress, electric displacement, and magnetic inductions in the vicinity of the magneto-electro-elastic dislocation are derived. The solutions are used to derive singular integral equations for the FGMEE layer containing multiple cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface by converting them to a system of linear algebraic equations. Finally, a numerical Laplace inversion algorithm is employed to determine the dynamic stress intensity factor. Numerical examples demonstrate the effects of the non-homogeneity parameter of the FGMEE layer, applied electric and magnetic loads, and the crack geometry on the dynamic stress intensity. This solution can be used as a Green's function to solve transient problems involving multiple cracks in a functionally graded magneto-electro-elastic layer.

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“…Laplace operator. To facilitate the solution of the above equations, it is convenient to use the following definitions 22 :…”

Section: Problem Statementmentioning

confidence: 99%

Section: Derivation Of the Integral Equations For Multiple Cracks Pro...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic response of cracked non‐homogeneous magneto‐electro‐elastic layer sandwiched by two dissimilar orthotropic layers

Arhani

Ayatollahi

2022

Fatigue Fract Eng Mat Struct

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“…The crack with an arbitrary position in a rectangular piezoelectric plane is the subject of research by Li and Lee. 12 Milan and Ayatollahi 13 considered the two distinct nonhomogeneous MEE layers with several interfacial cracks under impermeable conditions. The authors investigated the effects of the FG exponent of the two bonded layers and the cracks' interaction on the dynamic SIFs (DSIFs).…”

Section: Introductionmentioning

confidence: 99%

Transient analysis of a cracked functionally graded magneto‐electro‐elastic rectangular finite plane under anti‐plane mechanical and in‐plane electric and magnetic impacts

Ayatollahi,

Abdel‐Wahab,

Hashemi

2023

Fatigue Fract Eng Mat Struct

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The transient anti‐plane problem of a functionally graded magneto‐electro‐elastic (FGMEE) rectangular plane weakened by several embedded and edge cracks under various boundary conditions is solved. First, the solutions to the dynamic magneto‐electro‐elastic dislocation in the finite rectangular domain are derived by employing Laplace and finite Fourier cosine transforms. The solutions can be utilized to construct the singular integral equations in Laplace transform domain for FGMEE rectangular plane with multiple embedded and edge cracks. The integral equations arising from dislocation solutions have Cauchy‐type singularities with unknown dislocation density functions. These unknown functions may be obtained by reducing the integral equations into a system of linear algebraic equations, hereby, the dynamic stress intensity factors (DSIFs) for several arbitrarily embedded and edge cracks are obtained. The overshoots of dynamic stress intensity factors are shown to be intensely affected by the rectangular plane dimensions, length and position of the cracks, loading parameter, and negative or positive gradient index.

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“…On the theoretical methods to the dynamic fracture properties of piezoelectric/piezomagnetic strips or plane containing defects, some scholars have conducted in-depth explorations. The commonly used methods are Hankel transform [1], the boundary integral equation method [2,3], Fourier transform [4,5], and distributed dislocation technique [6,7]. In addition, the most widely studied loads are in-plane electrical and magnetic loads, and anti-plane mechanical loads [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Dynamic fracture behavior for hole-initiated cracks in functionally graded magneto-electro-elastic bi-materials

An,

Chen,

Zhang

et al. 2023

Mathematics and Mechanics of Solids

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In this article, the dynamic fracture behavior of hole-initiated cracks in functionally graded magneto-electro-elastic (FGMEE) bi-materials with exponential variation is studied by Green’s function method, and SH-wave is considered as an external load acting on the bi-materials. The mechanical model of the cracks is constructed through interface-conjunction and crack-deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips is expressed. Numerical results clarified the factors that affect the DSIF, including wave number, incident angle, the geometry of the defect, and the gradient of the bi-materials. The accuracy of the present methods is examined by comparing the obtained results with the reference solutions. Compared with previous traditional numerical and analytical methods, the methods proposed in this paper are relatively more effective and applicable, and provide a new perspective for studying the fracture problems of FGMEE materials with more complex defects in practical engineering.

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Transient analysis of multiple interface cracks between two dissimilar functionally graded magneto-electro-elastic layers

Cited by 11 publications

References 22 publications

Dynamic response of cracked non‐homogeneous magneto‐electro‐elastic layer sandwiched by two dissimilar orthotropic layers

Dynamic response of cracked non‐homogeneous magneto‐electro‐elastic layer sandwiched by two dissimilar orthotropic layers

Transient analysis of a cracked functionally graded magneto‐electro‐elastic rectangular finite plane under anti‐plane mechanical and in‐plane electric and magnetic impacts

Dynamic fracture behavior for hole-initiated cracks in functionally graded magneto-electro-elastic bi-materials

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