International Journal of Fracture

, Volume 162, Issue 1, pp 219–227

Crack nucleation in a peridynamic solid

Original Paper

DOI: 10.1007/s10704-010-9447-z

Cite this article as:
Silling, S.A., Weckner, O., Askari, E. et al. Int J Fract (2010) 162: 219. doi:10.1007/s10704-010-9447-z


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.


Crack nucleationMaterial stabilityPeridynamicElasticity

Mathematics Subject Classification (2000)


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