  Frictional granular matter is shown to be fundamentally different in its
plastic responses to external strains from generic glasses and amorphous solids
without friction. While regular glasses exhibit plastic instabilities due to a
vanishing of a real eigenvalue of the Hessian matrix, frictional granular
materials can exhibit a previously unnoticed additional mechanism for
instabilities, i.e. the appearance of a pair of complex eigenvalues leading to
oscillatory exponential growth of perturbations which are tamed by dynamical
nonlinearities. This fundamental difference appears crucial for the
understanding of plasticity and failure in frictional granular materials. The
possible relevance to earthquake physics is discussed.
