Magnetoelectroelastodynamic interaction of multiple arbitrarily oriented planar cracks

Athanasius, L.; Ang, W.T.

doi:10.1016/j.apm.2013.02.013

Cited by 3 publications

(7 citation statements)

References 18 publications

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“…Guided by the notation in Barnett and Lothe for electroelasticity, we define the generalized displacements

U_{J}

and stresses

S_{I j}

as (see, for example, Athanasius and Ang and Hattori and Sáez)

\begin{matrix} true \\ right U_{J} & = & left \{\begin{matrix} left u_{j} & left for J = j = 1, 2, \\ left ϕ & left for J = 3, \\ left φ & left for J = 4 . \end{matrix} \\ right S_{I j} & = & left \{\begin{matrix} left σ_{I j} & left for I = i = 1, 2, \\ left D_{j} & left for I = 3, \\ left B_{j} & left for I = 4 . \end{matrix} \end{matrix}

Furthermore, if we define

C_{I j K p}

C_{I j K p} = \{\begin{matrix} left c_{11} & left if false(I, j, K, p false) = false(1, 1, 1, 1 false), \\ left c_{12} & left if false(I, j, K, p false) = false(1, 1, 2, 2 false) = false(2, 2, 1, 1 false), \\ left c_{22} & left if false(I, j, K, p false) = false(2, 2, 2, 2 false), \\ left c_{44} & left if false(I, j, K, p false) = \end{matrix}

…”

Section: Boundary Value Problemmentioning

confidence: 99%

“…The problem of interest is to estimate the effective properties of the interface in the macro-models given in (6), (8), (9), and (10) by taking into account details of the interfacial micro-cracks. The effective properties can be computed once the jumps in the elastic displacement, the electric potential and the magnetic potentials across opposite micro-crack faces are determined by solving a boundary value problem governed by (5) subject to suitably prescribed conditions on the micro-cracks.…”

Section: The Problem and Basic Equations Of Magnetoelectroelasticit Ymentioning

confidence: 99%

“…Guided by the notation in Barnett and Lothe [6] for electroelasticity, we define the generalized displacements and stresses as (see, for example, Athanasius and Ang [5] and Hattori and Sáez [14]…”

Section: Boundary Value Problemmentioning

confidence: 99%

“…Such a distribution (that is, a 2 ( ) distribution of a smaller value of ) can give rise to a more realistic simulation for the variation of micro-crack lengths. Thus, we use 2 (5) to generate the lengths of the micro-cracks. Once the lengths are generated, the micro-cracks are randomly positioned over the interval 0 < 1 < .…”

Section: Statistical Simulationsmentioning

confidence: 99%

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Effective properties of magnetoelectroelastic interfaces weakened by micro‐cracks

2017

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The effective properties of a microscopically damaged interface between two dissimilar magnetoelectroelastic materials are investigated using a micro‐statistical model. The interface is modeled as damaged by a periodic array of micro‐cracks. The micro‐cracks over a period interval of the interface are randomly generated and are either all (i) magnetically and electrically impermeable, or (ii) magnetically permeable and electrically impermeable, or (iii) electrically permeable and magnetically impermeable, or (iv) magnetically and electrically permeable. The conditions on the micro‐cracks are formulated in terms of hypersingular integro‐differential equations with the jumps in the elastic displacements, the electric potential and the magnetic potential across opposite micro‐crack faces being unknown functions to be determined. Once the unknown functions are determined, the effective properties of the microscopically damaged interface can be readily computed. The effects of the crack density and the material constants on the effective properties are investigated in detail.

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“…Guided by the notation in Barnett and Lothe for electroelasticity, we define the generalized displacements

U_{J}

and stresses

S_{I j}

as (see, for example, Athanasius and Ang and Hattori and Sáez)

\begin{matrix} true \\ right U_{J} & = & left \{\begin{matrix} left u_{j} & left for J = j = 1, 2, \\ left ϕ & left for J = 3, \\ left φ & left for J = 4 . \end{matrix} \\ right S_{I j} & = & left \{\begin{matrix} left σ_{I j} & left for I = i = 1, 2, \\ left D_{j} & left for I = 3, \\ left B_{j} & left for I = 4 . \end{matrix} \end{matrix}

Furthermore, if we define

C_{I j K p}

C_{I j K p} = \{\begin{matrix} left c_{11} & left if false(I, j, K, p false) = false(1, 1, 1, 1 false), \\ left c_{12} & left if false(I, j, K, p false) = false(1, 1, 2, 2 false) = false(2, 2, 1, 1 false), \\ left c_{22} & left if false(I, j, K, p false) = false(2, 2, 2, 2 false), \\ left c_{44} & left if false(I, j, K, p false) = \end{matrix}

…”

Section: Boundary Value Problemmentioning

confidence: 99%

Section: The Problem and Basic Equations Of Magnetoelectroelasticit Ymentioning

confidence: 99%

Section: Boundary Value Problemmentioning

confidence: 99%

Section: Statistical Simulationsmentioning

confidence: 99%

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Effective properties of magnetoelectroelastic interfaces weakened by micro‐cracks

2017

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“…In recent years, an area of increasing interest is the fracture mechanics of magnetoelectroelastic materials, which combine the ferromagnetic and ferroelectric phases. For inclusions and cracks embedded in such magnetoelectroelastic solids, magnetoelectroelastic behaviors have been analyzed by many researchers including Wang et al [1], Wan et al [2],Zhong and Li [3], Huang et al [4], Gao et al [5], Sih et al [6], Li and Lee [7], Athanasius and Ang [8], Bhargava and Sharma [9], Tupholme [10], Wang and Mai [11], Zheng et al [12], Ma et al [13] and Li et al [14] . It can be found that only the crack tip singular field is involved in the researches mentioned above.…”

Section: Introductionmentioning

confidence: 99%

The Crack Tip Fields for Anti-plane Crack in Functionally Graded Magnetoelectroelastic Materials

Shen¹,

Xiao²,

Zhang³

2018

Proceedings of the 4th Annual International Conference on Material Engineering and Application (ICMEA 2017)

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The problem of a anti-plane crack in functionally graded magnetoelectroelastic materials is investigated. The material properties of the functionally graded magnetoelectroelastic materials are assumed to be exponential function of y perpendicular to the crack. To make the analysis tractable, the crack surface condition is assumed to be electrically and magnetically impermeable. The high order crack tip fields are obtained by the method of eigen-expansion method. This study has fundamental significance as Williams' solution.

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Transient Response of an Inﬁnite Isotropic Magneto-Electro-Elastic Material with Multiple Axisymmetric Planar Cracks

Vahdati,

Salehi,

Vahabi

et al. 2024

Preprint

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Dynamic behavior of coaxial axisymmetric planar cracks in the transversely isotropic magneto-electro-elastic (MEE) material in transient in-plane magneto-electro-mechanical loading is studied. Magneto-electrically impermeable as well as permeable cracks are assumed for crack surface. In the first step, considering prismatic and radial dynamic dislocations, electric and magnetic jumps are obtained through Laplace and Hankel transforms. These solutions are utilized to derive singular integral equations in the Laplace domain for the axisymmetric penny-shaped and annular cracks. Derived Cauchy singular type integral equations are solved to obtain the density of dislocation on the crack surfaces. Dislocation densities are utilized in computation of the dynamic stress intensity factors, electric displacement and magnetic induction in the vicinity tips of crack tips. Finally, some numerical case studies of a single and multiple cracks are presented. The effect of system parameters on the results is then discussed.

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Magnetoelectroelastodynamic interaction of multiple arbitrarily oriented planar cracks

Cited by 3 publications

References 18 publications

Effective properties of magnetoelectroelastic interfaces weakened by micro‐cracks

Effective properties of magnetoelectroelastic interfaces weakened by micro‐cracks

The Crack Tip Fields for Anti-plane Crack in Functionally Graded Magnetoelectroelastic Materials

Transient Response of an Inﬁnite Isotropic Magneto-Electro-Elastic Material with Multiple Axisymmetric Planar Cracks

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