International Journal of Fracture

, Volume 162, Issue 1–2, pp 219–227 | Cite as

Crack nucleation in a peridynamic solid

Original Paper

Abstract

A condition for the emergence of a discontinuity in an elastic peridynamic body is proposed, resulting in a material stability condition for crack nucleation. The condition is derived by determining whether a small discontinuity in displacement, superposed on a possibly large deformation, grows over time. Stability is shown to be determined by the sign of the eigenvalues of a tensor field that depends only on the linearized material properties. This condition for nucleation of a discontinuity in displacement can be interpreted in terms of the dynamic stability of plane waves with very short wavelength. A numerical example illustrates that cracks in a peridynamic body form spontaneously as the body is loaded.

Keywords

Crack nucleation Material stability Peridynamic Elasticity 

Mathematics Subject Classification (2000)

74B15 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • S. A. Silling
    • 1
  • O. Weckner
    • 2
  • E. Askari
    • 2
  • F. Bobaru
    • 3
  1. 1.Sandia National LaboratoriesAlbuquerqueUSA
  2. 2.The Boeing CompanySeattleUSA
  3. 3.University of Nebraska – LincolnLincolnUSA

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