On the stationary behaviour of the stress invariants (Q1086000)

Stress rate plays an important role in continuum mechanics, it appears in the constitutive law of complex materials. Historically there were proposed many definitions for stress rates. Prager claimed that within the rates discussed by him, only a vanishing stress rate according to the definition of Zaremba-Jaumann results in stationary behaviour of the Cauchy stress invariants, (for brevity called ''stationary condition''), so that the Zaremba-Jaumann stress rate seems to occupy a special situation. The discussion about this condition is meaningful, because it is always expected that the yield function in the constitutive law of plasticity should be stationary when the corresponding stress rate vanishes. In this note it is proved that many stress rates exist, which satisfy also this ''stationary condition''.