Mechanical & Materials Engineering, Department of


Date of this Version



Published in International Journal of Fracture (2010) 162:219–227; DOI 10.1007/s10704-010-9447-z Published by Springer Science+Business Media B.V. This article is a U.S. government work, and is not subject to copyright in the United States.


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.