BEM Solutions of Crack Problems in Gradient Elasticity

  • Gerasimos F. Karlis
  • Stephanos V. Tsinopoulos
  • Demosthenes Polyzos
  • Dimitri E. Beskos
Conference paper

Abstract

In this paper a boundary element method is used to solve gradient elastic fracture mechanics problems under static loading in three dimensions. A simplified version of Mindlinx2019;s Form II higher order gradient elastic theory is exploited and the Boundary Element Method (BEM), recently proposed by Polyzos et al. (2003) and Tsepoura et al. (2003), is utilized for the solution of Mode I gradient elastic problem. The Stress Intensity Factors (SIFs) are determined with the aid of a new special variable-order singularity discontinuous element applied at the tip of the crack. This element is designed to deal with fields that have different orders of singularities, as it is the case for displacement and traction fields in classical elastic case. Finally, a numerical example concerning the SIF calculation of a 3D mode I crack is presented.

Keywords

Gradient elasticity BEM Fracture mechanics Microstructure 3D mode I crack 

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References

  1. 1.
    Exadaktylos GE, Vardoulakis I (2001) Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics. Technophysics 335: 81–109.CrossRefADSGoogle Scholar
  2. 2.
    Mindlin RD (1964) Microstructure in linear elasticity. Arch Rat Mech Anal 10:51–78.MathSciNetGoogle Scholar
  3. 3.
    Vardoulakis I, Exadaktylos GE, Aifantis ED (1996) Gradient elasticity with surface energy: mode III crack problem. Int J Solid Struct 33:4531–4539.MATHCrossRefGoogle Scholar
  4. 4.
    Polyzos D, Tsepoura KG, Tsinopoulos SV, Beskos DE (2003) A boundary element method for solving 2-D and 3-D static gradient elastic problems. Part I: integral formulation. Comp Meth Appl Mech Eng 192(26–27):2845–2873.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Tsepoura KG, Tsinopoulos SV, Polyzos D, Beskos DE (2003) A boundary element method for solving 2-D and 3-D static gradient elastic problems. Part II: numerical implementation. Comp Meth Appl Mech Eng 192(26–27):2875–2907.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Karlis GF, Tsinopoulos SV, Polyzos D, Beskos DE (2007) Boundary element analysis of mode I and mixed mode (I and II) crack problems of 2-D gradient elasticity. Comput Meth Appl Mech Eng 196:5092–5103.CrossRefGoogle Scholar
  7. 7.
    Lim KM, Lee KH, Tay AAO, Zhou W (2002) A new variable-order singular boundary element for two-dimensional stress analysis. Int J Numer Meth Eng 55:293–316.MATHCrossRefGoogle Scholar
  8. 8.
    Zhou W, Lim KM, Lee KH, Tay AAO (2005) A new variable-order singular boundary element for calculating stress intensity factors in three-dimensional elasticity problems. Int J Solid Struct 42:159–185.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Barenblatt GI (1962) Mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V 2009

Authors and Affiliations

  • Gerasimos F. Karlis
    • 1
  • Stephanos V. Tsinopoulos
    • 2
  • Demosthenes Polyzos
    • 1
    • 3
  • Dimitri E. Beskos
    • 4
  1. 1.Department of Mechanical and Aeronautical EngineeringUniversity of PatrasPatrasGreece
  2. 2.Department of Mechanical EngineeringTechnological and Educational Institute of PatrasPatrasGreece
  3. 3.Institute of Chemical Engineering and High Temperature Chemical ProcessPatrasGreece
  4. 4.Department of Civil EngineeringUniversity of PatrasPatrasGreece

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