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

N. Jamia, Sami El-Borgi, M. Rekik, S. Usman

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)126-142
Number of pages17
JournalTheoretical and Applied Fracture Mechanics
Volume74
Issue number1
DOIs
Publication statusPublished - 2014

Fingerprint

Mixed Mode
Elastic Material
surface cracks
Crack
cracks
Surface Crack
Cracks
crack tips
Mechanical Stress
magnetic flux
integral equations
Crack Tip
Schmidt method
elastic properties
Magnetic flux
Elasticity
Integral Equations
Jump
Crack tips
hypergeometric functions

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

@article{282a5c61cdf64c46affbbb83ca0543cd,
title = "Investigation of the behavior of a mixed-mode crack in a functionally graded magneto-electro-elastic material by use of the non-local theory",
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.",
keywords = "Electric displacement, Functionally graded magneto-electro-elastic material (FGMEEM), Magnetic flux, Mechanical stress, Mixed-mode crack, Non-local theory",
author = "N. Jamia and Sami El-Borgi and M. Rekik and S. Usman",
year = "2014",
doi = "10.1016/j.tafmec.2014.09.002",
language = "English",
volume = "74",
pages = "126--142",
journal = "Theoretical and Applied Fracture Mechanics",
issn = "0167-8442",
publisher = "Elsevier",
number = "1",

}

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

VL - 74

SP - 126

EP - 142

JO - Theoretical and Applied Fracture Mechanics

JF - Theoretical and Applied Fracture Mechanics

SN - 0167-8442

IS - 1

ER -