International Journal of Fracture

, Volume 189, Issue 1, pp 103–110 | Cite as

Validity of linear elasticity in the crack-tip region of ideal brittle solids

  • Gaurav SinghEmail author
  • James R. Kermode
  • Alessandro De Vita
  • Robert W. Zimmerman
Brief Note


It is a well known that, according to classical elasticity, the stress in the crack-tip region is singular, which has led to a debate over the validity of linear elasticity in this region. In this work, comparisons of finite and small strain theories have been made in the crack-tip region of a brittle crystal to comment on the validity of linear elasticity in the crack tip region. We find that linear elasticity is capable of accurately defining the state of stress very close (\(\sim \)1 nm) to a static crack tip.


Crack Singularity Elasticity Brittle 



We acknowledge funding from the Rio Tinto Centre for Advanced Mineral Recovery based at Imperial College, London, and useful discussions with Gert van Hout throughout the project. J.R.K and A.D.V. acknowledge funding from the EPSRC HEmS Grant EP/L014742/1 and from the European Commission ADGLASS FP7 project.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Gaurav Singh
    • 1
    Email author
  • James R. Kermode
    • 2
  • Alessandro De Vita
    • 2
    • 3
  • Robert W. Zimmerman
    • 1
  1. 1.Department of Earth Science and EngineeringImperial College LondonLondonUK
  2. 2.Department of PhysicsKing’s College LondonLondonUK
  3. 3.CENMAT-UTSTriesteItaly

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