Hello All:

I'm interested in learning more about material instability, for example the localization criterions of Hill (1962) and Rudnicki and Rice (1975).  I also am aware of work by Rice (1976), in which a perturbation is made to the displacement field in the form of a plane harmonic wave, resulting in a strong ellipticity instability condition that looks like Det(Q), where Q = c_ijkl + Sigma_jk, i.e. a competition between material softening and stress increase determines the instability.  Furthermore, this stability criterion is developed assuming an infinite body.