Bifurcations in elastic-plastic materials (Q1802881)

Localized deformations of elastic-plastic structures with hardening lead to failure with continued loading. This localization is often associated with satisfaction of the classical discontinuous bifurcation Drucker criterion, that's, with the loss of positive definiteness of the rate of second order work. The authors propose that the strong ellipticity criterion should be used in place of the classical discontinuous bifurcation criterion as a necessary condition for localization.