### Abstract

This paper investigates the problem of an axisymmetric penny shaped crack embedded in an infinite functionally graded magneto electro elastic medium. The loading consists of magnetoelectromechanical loads applied on the crack surfaces assumed to be magneto electrically impermeable. The material's gradient is parallel to the axisymmetric direction and is perpendicular to the crack plane. An anisotropic constitutive law is adopted to model the material behavior. The governing equations are converted analytically using Hankel transform into coupled singular integral equations, which are solved numerically to yield the crack tip stress, electric displacement and magnetic induction intensity factors. A similar problem but with a different crack morphology, that is a plane crack embedded in an infinite functionally graded magneto electro elastic medium, was considered by the authors in a previous work (Rekik et al., 2012) [25]. While the overall solution schemes look similar, the axisymmetric problem resulted in more mathematical complexities and let to different conclusions with respect to the influence of coupling between elastic, electric and magnetic effects. The main focus of this paper is to study the effect of material non-homogeneity on the fields' intensity factors to understand further the behavior of graded magnetoelectroelastic materials containing penny shaped cracks and to inspect the effect of varying the crack geometry.

Original language | English (US) |
---|---|

Pages (from-to) | 1193-1210 |

Number of pages | 18 |

Journal | Applied Mathematical Modelling |

Volume | 38 |

Issue number | 4 |

DOIs | |

State | Published - Feb 15 2014 |

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### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Applied Mathematics

### Cite this

*Applied Mathematical Modelling*,

*38*(4), 1193-1210. https://doi.org/10.1016/j.apm.2013.08.006

}

*Applied Mathematical Modelling*, vol. 38, no. 4, pp. 1193-1210. https://doi.org/10.1016/j.apm.2013.08.006

**An axisymmetric problem of an embedded mixed-mode crack in a functionally graded magnetoelectroelastic infinite medium.** / Rekik, M.; El-Borgi, S.; Ounaies, Zoubeida.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An axisymmetric problem of an embedded mixed-mode crack in a functionally graded magnetoelectroelastic infinite medium

AU - Rekik, M.

AU - El-Borgi, S.

AU - Ounaies, Zoubeida

PY - 2014/2/15

Y1 - 2014/2/15

N2 - This paper investigates the problem of an axisymmetric penny shaped crack embedded in an infinite functionally graded magneto electro elastic medium. The loading consists of magnetoelectromechanical loads applied on the crack surfaces assumed to be magneto electrically impermeable. The material's gradient is parallel to the axisymmetric direction and is perpendicular to the crack plane. An anisotropic constitutive law is adopted to model the material behavior. The governing equations are converted analytically using Hankel transform into coupled singular integral equations, which are solved numerically to yield the crack tip stress, electric displacement and magnetic induction intensity factors. A similar problem but with a different crack morphology, that is a plane crack embedded in an infinite functionally graded magneto electro elastic medium, was considered by the authors in a previous work (Rekik et al., 2012) [25]. While the overall solution schemes look similar, the axisymmetric problem resulted in more mathematical complexities and let to different conclusions with respect to the influence of coupling between elastic, electric and magnetic effects. The main focus of this paper is to study the effect of material non-homogeneity on the fields' intensity factors to understand further the behavior of graded magnetoelectroelastic materials containing penny shaped cracks and to inspect the effect of varying the crack geometry.

AB - This paper investigates the problem of an axisymmetric penny shaped crack embedded in an infinite functionally graded magneto electro elastic medium. The loading consists of magnetoelectromechanical loads applied on the crack surfaces assumed to be magneto electrically impermeable. The material's gradient is parallel to the axisymmetric direction and is perpendicular to the crack plane. An anisotropic constitutive law is adopted to model the material behavior. The governing equations are converted analytically using Hankel transform into coupled singular integral equations, which are solved numerically to yield the crack tip stress, electric displacement and magnetic induction intensity factors. A similar problem but with a different crack morphology, that is a plane crack embedded in an infinite functionally graded magneto electro elastic medium, was considered by the authors in a previous work (Rekik et al., 2012) [25]. While the overall solution schemes look similar, the axisymmetric problem resulted in more mathematical complexities and let to different conclusions with respect to the influence of coupling between elastic, electric and magnetic effects. The main focus of this paper is to study the effect of material non-homogeneity on the fields' intensity factors to understand further the behavior of graded magnetoelectroelastic materials containing penny shaped cracks and to inspect the effect of varying the crack geometry.

UR - http://www.scopus.com/inward/record.url?scp=84893752638&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893752638&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2013.08.006

DO - 10.1016/j.apm.2013.08.006

M3 - Article

AN - SCOPUS:84893752638

VL - 38

SP - 1193

EP - 1210

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 4

ER -