A SUFFICIENT CONDITION FOR THE LINEAR INSTABILITY OF STRAIN-RATE-DEPENDENT SOLIDS

The linear stability criterion proposed generalizes to continua earlie r results obtained for the viscoplastic Shanley column. A sufficient c ondition for instability is marked by the change of sign of the real p art of the dominant eigenvalue for the system of equations constructed from the linearized version of the first and second derivatives with respect to time of the principle of virtual work. In particular, it is shown that the conditions for first instability are those for the fir st bifurcation of a strain-rate-independent solid obtained in the limi t of inviscid plastic flow.