Crack nucleation in a peridynamic solid Authors S. A. Silling Sandia National Laboratories O. Weckner E. Askari F. Bobaru University of Nebraska – Lincoln Original Paper

First Online: 28 January 2010 Received: 03 August 2009 Accepted: 05 January 2010 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
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

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