On crack propagation in orthotropic media for degenerate states

The objective of this paper is to investigate a critical point, in the topic of crack dynamics in brittle orthotropic media, which occurs in the case of repeated elastodynamic eigenvalues. A proper analytical approach is introduced and a new complex variable representation of the elastodynamic fields in a degenerate state of propagation is provided. The obtained equations are applied to study the Mode-II elastodynamic problem of a steadily propagating shear crack in an orthotropic medium. Numerical results show that for some values of elastic constants degenerate states of crack propagation are physically admissible although unstable under perturbation of the instantaneous crack velocity.