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.
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Silling, S.A., Weckner, O., Askari, E. et al. Crack nucleation in a peridynamic solid. Int J Fract 162, 219–227 (2010). https://doi.org/10.1007/s10704-010-9447-z
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DOI: https://doi.org/10.1007/s10704-010-9447-z