T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms

Jeong Ho Kim, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a "generalized isoparametric formulation" and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions.

Original languageEnglish (US)
Pages (from-to)345-384
Number of pages40
JournalInternational Journal of Fracture
Issue number4
StatePublished - Apr 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


  • Finite element method (FEM)
  • Fracture mechanics
  • Functionally graded material (FGM)
  • Generalized isoparametric formulation (GIF).
  • Interaction integral
  • Orthotropic materials
  • T-stress
  • Two-state integral


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