Non-local behavior of two collinear mixed-mode limited-permeable cracks in a functionally graded piezoelectric medium

Nidhal Jamia, Sami El-Borgi, Shameem Usman

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this paper, the problem of two collinear mixed-mode limited-permeable cracks embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen's non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Employing the Fourier transform, the mixed-boundary value problem is converted into three integral equations for each crack, with the unknown variables being the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of the interaction of two cracks, material gradient parameter describing functionally graded piezoelectric materials and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Original languageEnglish
JournalApplied Mathematical Modelling
DOIs
Publication statusAccepted/In press - 23 Dec 2014

Fingerprint

Mixed Mode
Collinear
Piezoelectric Material
Crack
Cracks
Mechanical Stress
Surface Crack
Piezoelectric materials
Crack Tip
Integral Equations
Functionally graded materials
Crack tips
Unknown
Integral equations
Mixed Boundary Value Problem
Electric Potential
Jacobi Polynomials
Near-field
Classical Solution
Perpendicular

Keywords

  • Electric displacement
  • Functionally graded piezoelectric material (FGPM)
  • Mechanical stress
  • Non-local theory
  • Schmidt method
  • Two collinear mixed-mode limited-permeable cracks

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation

Cite this

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AB - In this paper, the problem of two collinear mixed-mode limited-permeable cracks embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen's non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Employing the Fourier transform, the mixed-boundary value problem is converted into three integral equations for each crack, with the unknown variables being the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of the interaction of two cracks, material gradient parameter describing functionally graded piezoelectric materials and lattice parameter on the mechanical stress and electric displacement field near crack tips.

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