Derivation of the normality rule for time-dependent deformation using the principle of maximal rate of entropy production

Abstract

Derivation of the normality rule for time-dependent deformation by the principle of the maximal rate of entropy production was carried out. The derivation was made within the framework of thermomechanics with internal variables. Since Ziegler did not cast his principle into an exact mathematical framework, it was done here. A condition for the multiplier in the normality rule (c.f. plasticity multiplier) was derived. If the condition gives a constant value for the multiplier, the specific (complementary) dissipation function was shown to be a homogeneous function. In the case where the value of the multiplier depends on the state variables, the dissipation potential is a non-homogeneous function.