Shakedown Under Thermomechanical Loads

Abstract

A shakedown theory for elastic–perfectly plastic structures subjected to thermomechanical loads varying within a given range is outlined under the assumption of temperature-dependent yield stress, but temperature-independent elastic moduli and thermal expansion coefficient are considered. Inertia and creep effects, along with thermal coupling phenomena, are considered negligible. A nonstandard constitutive model is used in which a central role is played by the yield function-assumed convex in the stress–temperature space. The inherent flow mechanism obeys the normality rule and includes, beside the standard plastic strain rates, an extra scalar variable work conjugate of the temperature, conventionally called plastic entropy rate, a measure of the reduction of the dissipation capacity of the material due to thermal softening. The static and kinematic shakedown theorems are formulated and proved within the present context.