On the eigenvalues of the acoustic tensor in elastoplasticity

A technique is presented to perform the spectral analysis of the acoustic tensor for the loading branch of a generic elastic plastic solid at finite strain, with general associative and non associative flow rule. The spectral analysis applies to general three dimensional deformations, under the hypotheses that the elastic acoustic tensor be symmetric, and that an acoustical axis is always coincident with a neutral plastic wave amplitude. Moreover, the spectral analysis applies, without the latter restriction, to two dimensional theories of elastoplasticity. Under these conditions, the occurrence of complex eigenvalues (flutter instability) is specified in terms of a necessary and sufficient condition. The onset of flutter (coalescence of two eigenvalues) is proved to be possible, under broad conditions