### Abstract

In this paper, we consider the problem of a mixed-mode crack embedded in an infinite medium made of a functionally graded magneto-electro-elastic material (FGMEEM) with the crack surfaces subjected to magneto-electro-mechanical loadings. Eringen's non-local theory of elasticity is applied to obtain the governing magneto-electro-elastic equations. To make the analysis tractable, it is assumed that the magneto-electro-elastic material properties vary exponentially along a perpendicular plane to the crack. Using Fourier transform, the resulting mixed-boundary value problem is converted into four integral equations, in which the unknown variables are the jumps of mechanical displacements, electric and magnetic potentials across the crack surfaces. To solve the integral equations, the jumps of displacements and electric and magnetic potential across crack surfaces are directly expanded in a series of Jacobi polynomials and the resulting equations are solved using the Schmidt method. Unlike classical magnetic, electric and elasticity solutions, it is found that no mechanical stress, electric displacement and magnetic flux singularities are present at the crack tips. This enables the use of the maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing functionally graded materials and lattice parameter on the mechanical stress, magnetic flux and electric displacement field near crack tips.

Original language | English |
---|---|

Pages (from-to) | 126-142 |

Number of pages | 17 |

Journal | Theoretical and Applied Fracture Mechanics |

Volume | 74 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 |

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### Keywords

- Electric displacement
- Functionally graded magneto-electro-elastic material (FGMEEM)
- Magnetic flux
- Mechanical stress
- Mixed-mode crack
- Non-local theory

### ASJC Scopus subject areas

- Applied Mathematics
- Materials Science(all)
- Condensed Matter Physics
- Mechanical Engineering

### Cite this

*Theoretical and Applied Fracture Mechanics*,

*74*(1), 126-142. https://doi.org/10.1016/j.tafmec.2014.09.002

**Investigation of the behavior of a mixed-mode crack in a functionally graded magneto-electro-elastic material by use of the non-local theory.** / Jamia, N.; El-Borgi, Sami; Rekik, M.; Usman, S.

Research output: Contribution to journal › Article

*Theoretical and Applied Fracture Mechanics*, vol. 74, no. 1, pp. 126-142. https://doi.org/10.1016/j.tafmec.2014.09.002

}

TY - JOUR

T1 - Investigation of the behavior of a mixed-mode crack in a functionally graded magneto-electro-elastic material by use of the non-local theory

AU - Jamia, N.

AU - El-Borgi, Sami

AU - Rekik, M.

AU - Usman, S.

PY - 2014

Y1 - 2014

N2 - In this paper, we consider the problem of a mixed-mode crack embedded in an infinite medium made of a functionally graded magneto-electro-elastic material (FGMEEM) with the crack surfaces subjected to magneto-electro-mechanical loadings. Eringen's non-local theory of elasticity is applied to obtain the governing magneto-electro-elastic equations. To make the analysis tractable, it is assumed that the magneto-electro-elastic material properties vary exponentially along a perpendicular plane to the crack. Using Fourier transform, the resulting mixed-boundary value problem is converted into four integral equations, in which the unknown variables are the jumps of mechanical displacements, electric and magnetic potentials across the crack surfaces. To solve the integral equations, the jumps of displacements and electric and magnetic potential across crack surfaces are directly expanded in a series of Jacobi polynomials and the resulting equations are solved using the Schmidt method. Unlike classical magnetic, electric and elasticity solutions, it is found that no mechanical stress, electric displacement and magnetic flux singularities are present at the crack tips. This enables the use of the maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing functionally graded materials and lattice parameter on the mechanical stress, magnetic flux and electric displacement field near crack tips.

AB - In this paper, we consider the problem of a mixed-mode crack embedded in an infinite medium made of a functionally graded magneto-electro-elastic material (FGMEEM) with the crack surfaces subjected to magneto-electro-mechanical loadings. Eringen's non-local theory of elasticity is applied to obtain the governing magneto-electro-elastic equations. To make the analysis tractable, it is assumed that the magneto-electro-elastic material properties vary exponentially along a perpendicular plane to the crack. Using Fourier transform, the resulting mixed-boundary value problem is converted into four integral equations, in which the unknown variables are the jumps of mechanical displacements, electric and magnetic potentials across the crack surfaces. To solve the integral equations, the jumps of displacements and electric and magnetic potential across crack surfaces are directly expanded in a series of Jacobi polynomials and the resulting equations are solved using the Schmidt method. Unlike classical magnetic, electric and elasticity solutions, it is found that no mechanical stress, electric displacement and magnetic flux singularities are present at the crack tips. This enables the use of the maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing functionally graded materials and lattice parameter on the mechanical stress, magnetic flux and electric displacement field near crack tips.

KW - Electric displacement

KW - Functionally graded magneto-electro-elastic material (FGMEEM)

KW - Magnetic flux

KW - Mechanical stress

KW - Mixed-mode crack

KW - Non-local theory

UR - http://www.scopus.com/inward/record.url?scp=84922336621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922336621&partnerID=8YFLogxK

U2 - 10.1016/j.tafmec.2014.09.002

DO - 10.1016/j.tafmec.2014.09.002

M3 - Article

AN - SCOPUS:84922336621

VL - 74

SP - 126

EP - 142

JO - Theoretical and Applied Fracture Mechanics

JF - Theoretical and Applied Fracture Mechanics

SN - 0167-8442

IS - 1

ER -