The crack problem for nonhomogneous materials under antiplane shear loading - A displacement based formulation

Youn Sha Chan, Glaucio H. Paulino, Albert C. Fannjiang

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

This paper presents a displacement based integral equation formulation for the mode III crack problem in a non-homogeneous medium with a continuously differentiable shear modulus, which is assumed to be an exponential function, i.e., G(x) = Go exp(βx). This formulation leads naturally to a hypersingular integral equation. The problem is solved for a finite crack and results are given for crack profiles and stress intensity factors. The results are affected by the parameter β describing the material nonhomogeneity. This study is motivated by crack problems in strain-gradient elasticity theories where higher order singular integral equations naturally arise even in the slope-based formulation.

Original languageEnglish (US)
Pages (from-to)2989-3005
Number of pages17
JournalInternational Journal of Solids and Structures
Volume38
Issue number17
DOIs
StatePublished - Mar 7 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Keywords

  • Asymptotic analysis
  • Collocation method
  • Fredholm integral equation
  • Functionally graded materials
  • Hypersingular integrals
  • Integral equation method
  • Mode III crack
  • Stress intensity factors

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